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Diverse Behavior Path Graphs for Multi-Behavior Recommendation 认领 引用
1
作者 Qian Hu Lei Tan +2 位作者 Qingjun Yuan Zong Zuo Yan Li 《Computers, Materials & Continua》 SCIE EI 2026年第6期674-696,共23页
Multi-behavior recommendation methods leverage various types of user interaction behaviors to make personalized recommendations.Behavior paths formed by diverse user interactions reveal distinctive patterns between us... Multi-behavior recommendation methods leverage various types of user interaction behaviors to make personalized recommendations.Behavior paths formed by diverse user interactions reveal distinctive patterns between users and items.Modeling these behavioral paths captures multidimensional behavioral features,which enables accurate learning of user preferences and improves recommendation accuracy.However,existing methods share two critical limitations:(1)Lack of modeling for the diversity of behavior paths;(2)Ignoring the impact of item attribute information on user behavior paths.To address these issues,we propose a Directed Behavior path graph-based Multi-behavior Recommendation method(DBMR).Specifically,we first construct a directed user-item behavior path graph based on diverse behavior chains.For each behavior,we then build a user-item interaction graph and use a LightGCN model with residual design to learn user and item embeddings.Next,we introduce a graph attention message aggregator that integrates features from previous behaviors into the learning of the next behavior,weighted by the transition strength between behaviors.Finally,we compute the recommendation score from the user preference and item representations under the target behavior.We adopt a joint optimization framework with a multi-task learning strategy,which accounts for each auxiliary behavior’s contribution to target behavior prediction.Additionally,an auxiliary loss measures the difference between item embeddings from behavior paths and those from an attribute-feature encoder,thereby capturing multidimensional item features and refining recommendation results.Experiments on two real-world datasets demonstrate the effectiveness of our method in utilizing multi-behavior data. 展开更多
关键词 Multi-behavior recommendation diverse behavior path graphs joint optimization graph attention networks
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RSG-P:A Fast Global Path Planning Method Based on Route Scene Graph 认领 引用
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作者 TIAN Chensheng 《Journal of Shanghai Jiaotong university(Science)》 EI 2026年第4期881-897,I0006,共17页
road information in RSG,road pre-planning and multi-level planning can be used to accelerate global path planning.We evaluate the method in both simulation and real environments.Compared to the search-based methods Fa... road information in RSG,road pre-planning and multi-level planning can be used to accelerate global path planning.We evaluate the method in both simulation and real environments.Compared to the search-based methods Far Planner(1-10ms),A,DLite(10-100ms),and the random sampling-based methods BIT*,SPARS(10-100ms),the method achieved the sub-millisecond level(0.1-1 ms)planning speed in over 10000m2 scenarios. 展开更多
关键词 robot global path planning scene graph spatial connectivity routing planning
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Computation graph pruning based on critical path retention in evolvable networks 认领 引用
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作者 XIE Xiaoyan YANG Tianjiao +4 位作者 ZHU Yun LUO Xing JIN Luochen YU Jinhao REN Xun 《High Technology Letters》 EI CAS 2025年第3期266-272,共7页
The dynamic routing mechanism in evolvable networks enables adaptive reconfiguration of topol-ogical structures and transmission pathways based on real-time task requirements and data character-istics.However,the heig... The dynamic routing mechanism in evolvable networks enables adaptive reconfiguration of topol-ogical structures and transmission pathways based on real-time task requirements and data character-istics.However,the heightened architectural complexity and expanded parameter dimensionality in evolvable networks present significant implementation challenges when deployed in resource-con-strained environments.Due to the critical paths ignored,traditional pruning strategies cannot get a desired trade-off between accuracy and efficiency.For this reason,a critical path retention pruning(CPRP)method is proposed.By deeply traversing the computational graph,the dependency rela-tionship among nodes is derived.Then the nodes are grouped and sorted according to their contribu-tion value.The redundant operations are removed as much as possible while ensuring that the criti-cal path is not affected.As a result,computational efficiency is improved while a higher accuracy is maintained.On the CIFAR benchmark,the experimental results demonstrate that CPRP-induced pruning incurs accuracy degradation below 4.00%,while outperforming traditional feature-agnostic grouping methods by an average 8.98%accuracy improvement.Simultaneously,the pruned model attains a 2.41 times inference acceleration while achieving 48.92%parameter compression and 53.40%floating-point operations(FLOPs)reduction. 展开更多
关键词 evolvable network computation graph traversing dynamic routing critical path retention pruning
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Path Planning for Substation UAV Inspection Based on 3D Point Cloud Mapping 认领 引用
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作者 Yanping Chen Zhengxin Zhan +3 位作者 Xiaohui Yan Le Zou Yucheng Zhong Hailei Wang 《Computers, Materials & Continua》 SCIE EI 2026年第5期2138-2159,共22页
With the increasing complexity of substation inspection tasks,achieving efficient and safe path planning for Unmanned Aerial Vehicles in densely populated and structurally complex three-dimensional(3D)environments rem... With the increasing complexity of substation inspection tasks,achieving efficient and safe path planning for Unmanned Aerial Vehicles in densely populated and structurally complex three-dimensional(3D)environments remains a critical challenge.To address this problem,this paper proposes an improved path planning algorithm—Random Geometric Graph(RGG)-guided Rapidly-exploring Random Tree(R-RRT)—based on the classical Rapidly-exploring Random Tree(RRT)framework.First,a refined 3D occupancy grid map is constructed from Light Detection and Ranging point cloud data through ground filtering,noise removal,coordinate transformation,and obstacle inflation using spherical structuring elements.During the planning stage,a dynamic goal-biasing strategy is introduced to adaptively adjust the sampling direction,the sampling distribution is optimized using a pre-generated RGG,and collision detection is accelerated via a K-Dimensional Tree structure.After initial trajectory generation,redundant nodes are eliminated via greedy pruning,and a curvature-minimizing gradient-based optimizationmethod is applied to smooth the trajectory.Experimental results conducted in a simulated substation environment demonstrate that,compared with mainstream path planning algorithms,the proposed R-RRT achieves superior performance in terms of path length,planning time,and trajectory smoothness.Comprehensive analysis shows that the proposed method significantly enhances trajectory quality,planning efficiency,and operational safety,validating its applicability and advantages for high-precision 3D path planning in complex substation inspection scenarios. 展开更多
关键词 R-RRT algorithm unmanned aerial vehicles path planning random geometric graph 3D occupancy grid map substation inspection
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A multi-parametric path planning framework utilizing airspace visibility graphs for urban battlefield environments 认领 引用
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作者 Sidao Chen Xuejun Zhang +1 位作者 Zuyao Zhang Jianxiang Ma 《Defence Technology（防务技术）》 SCIE EI CAS CSCD 2025年第9期112-126,共15页
Urban combat environments pose complex and variable challenges for UAV path planning due to multidimensional factors,such as static and dynamic obstructions as well as risks of exposure to enemy detection,which threat... Urban combat environments pose complex and variable challenges for UAV path planning due to multidimensional factors,such as static and dynamic obstructions as well as risks of exposure to enemy detection,which threaten flight safety and mission success.Traditional path planning methods typically depend solely on the distribution of static obstacles to generate collision-free paths,without accounting for constraints imposed by enemy detection and strike capabilities.Such a simplified approach can yield safety-compromising routes in highly complex urban airspace.To address these limitations,this study proposes a multi-parameter path planning method based on reachable airspace visibility graphs,which integrates UAV performance constraints,environmental limitations,and exposure risks.An innovative heuristic algorithm is developed to balance operational safety and efficiency by both exposure risks and path length.In the case study set in a typical mixed-use urban area,analysis of airspace visibility graphs reveals significant variations in exposure risk at different regions and altitudes due to building encroachments.Path optimization results indicate that the method can effectively generate covert and efficient flight paths by dynamically adjusting the exposure index,which represents the likelihood of enemy detection,and the path length,which corresponds to mission execution time. 展开更多
关键词 UAV Path planning Urban battlefield environment Airspace visibility graph Isovist
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k-Product Cordial Labeling of Path Graphs 认领 引用
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作者 Robinson Santrin Sabibha Kruz Jeya Daisy +1 位作者 Pon Jeyanthi Maged Zakaria Youssef 《Open Journal of Discrete Mathematics》 2025年第1期1-29,共29页
In 2012, Ponraj et al. defined a concept of k-product cordial labeling as follows: Let f be a map from V(G)to { 0,1,⋯,k−1 }where k is an integer, 1≤k≤| V(G) |. For each edge uvassign the label f(u)f(v)(modk). f is c... In 2012, Ponraj et al. defined a concept of k-product cordial labeling as follows: Let f be a map from V(G)to { 0,1,⋯,k−1 }where k is an integer, 1≤k≤| V(G) |. For each edge uvassign the label f(u)f(v)(modk). f is called a k-product cordial labeling if | vf(i)−vf(j) |≤1, and | ef(i)−ef(j) |≤1, i,j∈{ 0,1,⋯,k−1 }, where vf(x)and ef(x)denote the number of vertices and edges respectively labeled with x (x=0,1,⋯,k−1). Motivated by this concept, we further studied and established that several families of graphs admit k-product cordial labeling. In this paper, we show that the path graphs Pnadmit k-product cordial labeling. 展开更多
关键词 Cordial Labeling Product Cordial Labeling k-Product Cordial Labeling Path Graph
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Heuristic Expanding Disconnected Graph:A Rapid Path Planning Method for Mobile Robots 认领 引用 被引量：4
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作者 Yong Tao Lian Duan +3 位作者 He Gao Yufan Zhang Yian Song Tianmiao Wang 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2024年第2期68-82,共15页
Existing mobile robots mostly use graph search algorithms for path planning,which suffer from relatively low planning efficiency owing to high redundancy and large computational complexity.Due to the limitations of th... Existing mobile robots mostly use graph search algorithms for path planning,which suffer from relatively low planning efficiency owing to high redundancy and large computational complexity.Due to the limitations of the neighborhood search strategy,the robots could hardly obtain the most optimal global path.A global path planning algorithm,denoted as EDG*,is proposed by expanding nodes using a well-designed expanding disconnected graph operator(EDG)in this paper.Firstly,all obstacles are marked and their corners are located through the map pre-processing.Then,the EDG operator is designed to find points in non-obstruction areas to complete the rapid expansion of disconnected nodes.Finally,the EDG*heuristic iterative algorithm is proposed.It selects the candidate node through a specific valuation function and realizes the node expansion while avoiding collision with a minimum offset.Path planning experiments were conducted in a typical indoor environment and on the public dataset CSM.The result shows that the proposed EDG*reduced the planning time by more than 90%and total length of paths reduced by more than 4.6%.Compared to A*,Dijkstra and JPS,EDG*does not show an exponential explosion effect in map size.The EDG*showed better performance in terms of path smoothness,and collision avoidance.This shows that the EDG*algorithm proposed in this paper can improve the efficiency of path planning and enhance path quality. 展开更多
关键词 Global path planning Mobile robot Expanding disconnected graph Edge node Offset
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3D multipath planning for UAV based on network graph 认领 引用 被引量：1
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作者 Xin Liu Chengping Zhou Mingyue Ding 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2011年第4期640-646,共7页
According to the characteristic and the requirement of multipath planning, a new multipath planning method is proposed based on network. This method includes two steps： the construction of network and multipath searc... According to the characteristic and the requirement of multipath planning, a new multipath planning method is proposed based on network. This method includes two steps： the construction of network and multipath searching. The construction of network proceeds in three phases： the skeleton extraction of the configuration space, the judgment of the cross points in the skeleton and how to link the cross points to form a network. Multipath searching makes use of the network and iterative penalty method （IPM） to plan multi-paths, and adjusts the planar paths to satisfy the requirement of maneuverability of unmanned aerial vehicle （UAV）. In addition, a new height planning method is proposed to deal with the height planning of 3D route. The proposed algorithm can find multiple paths automatically according to distribution of terrain and threat areas with high efficiency. The height planning can make 3D route following the terrain. The simulation experiment illustrates the feasibility of the proposed method. 展开更多
关键词 path planning skeleton graph iterative penaltymethod （IPM） network graph.
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Personalized Learning Path Recommendations for Software Testing Courses Based on Knowledge Graphs 认领 引用 被引量：1
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作者 Wei Zheng Ruonan Gu +2 位作者 Xiaoxue Wu Lipeng Gao Han Li 《计算机教育》 2023年第12期63-70,共8页
Software testing courses are characterized by strong practicality,comprehensiveness,and diversity.Due to the differences among students and the needs to design personalized solutions for their specific requirements,th... Software testing courses are characterized by strong practicality,comprehensiveness,and diversity.Due to the differences among students and the needs to design personalized solutions for their specific requirements,the design of the existing software testing courses fails to meet the demands for personalized learning.Knowledge graphs,with their rich semantics and good visualization effects,have a wide range of applications in the field of education.In response to the current problem of software testing courses which fails to meet the needs for personalized learning,this paper offers a learning path recommendation based on knowledge graphs to provide personalized learning paths for students. 展开更多
关键词 Knowledge graphs Software testing Learning path Personalized education
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Expanding Hot Code Path for Data Cleaning on Software Graph 认领 引用
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作者 Guang Sun Xiaoping Fan +3 位作者 Wangdong Jiang Hangjun Zhou Fenghua Li Rong Yang 《Computers, Materials & Continua》 SCIE EI 2020年第5期743-753,共11页
Graph analysis can be done at scale by using Spark GraphX which loading data into memory and running graph analysis in parallel.In this way,we should take data out of graph databases and put it into memory.Considering... Graph analysis can be done at scale by using Spark GraphX which loading data into memory and running graph analysis in parallel.In this way,we should take data out of graph databases and put it into memory.Considering the limitation of memory size,the premise of accelerating graph analytical process reduces the graph data to a suitable size without too much loss of similarity to the original graph.This paper presents our method of data cleaning on the software graph.We use SEQUITUR data compression algorithm to find out hot code path and store it as a whole paths directed acyclic graph.Hot code path is inherent regularity of a program.About 10 to 200 hot code path account for 40%-99%of a program’s execution cost.These hot paths are acyclic contribute more than 0.1%-1.0%of some execution metric.We expand hot code path to a suitable size which is good for runtime and keeps similarity to the original graph. 展开更多
关键词 Hot code path expanded hot path software graph software graph
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Depth First:Optimal Path Discovery Between Designated Nodes in Random Ring-Based Graphs 认领 引用
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作者 Li Qi Xu Jiasheng +4 位作者 Zhang Haonan Kang Huquan Fu Luoyi Long Fei Wang Xinbing 《China Communications》 SCIE CSCD 2024年第9期225-241,共17页
This paper focuses on optimally determining the existence of connected paths between some given nodes in random ring-based graphs.Serving as a fundamental underlying structure in network modeling,ring topology appears... This paper focuses on optimally determining the existence of connected paths between some given nodes in random ring-based graphs.Serving as a fundamental underlying structure in network modeling,ring topology appears as commonplace in many realistic scenarios.Regarding this,we consider graphs composed of rings,with some possible connected paths between them.Without prior knowledge of the exact node permutations on rings,the existence of each edge can be unraveled through edge testing at a unit cost in one step.The problem examined is that of determining whether the given nodes are connected by a path or separated by a cut,with the minimum expected costs involved.Dividing the problem into different cases based on different topologies of the ring-based networks,we propose the corresponding policies that aim to quickly seek the paths between nodes.A common feature shared by all those policies is that we stick to going in the same direction during edge searching,with edge testing in each step only involving the test between the source and the node that has been tested most.The simple searching rule,interestingly,can be interpreted as a delightful property stemming from the neat structure of ring-based networks,which makes the searching process not rely on any sophisticated behaviors.We prove the optimality of the proposed policies by calculating the expected cost incurred and making a comparison with the other class of strategies.The effectiveness of the proposed policies is also verified through extensive simulations,from which we even disclose three extra intriguing findings:i)in a onering network,the cost will grow drastically with the number of designated nodes when the number is small and will grow slightly when that number is large;ii)in ring-based network,Depth First is optimal in detecting the connectivity between designated nodes;iii)the problem of multi-ring networks shares large similarity with that of two-ring networks,and a larger number of ties between rings will not influence the expected cost. 展开更多
关键词 connectivity analysis cost minimization path discover ring-based graph
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Longest Paths and Cycles in Connected Claw-Free Graphs 认领 引用
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作者 李明楚 李旭东 《Transactions of Tianjin University》 EI CAS 2004年第3期221-224,共4页
A graph is called claw-free if it does not contain a claw as its induced subgraph.In this paper, we prove the following results:1)If G is a 2-connected claw-free graph on n vertices,then for any vertex v and any two d... A graph is called claw-free if it does not contain a claw as its induced subgraph.In this paper, we prove the following results:1)If G is a 2-connected claw-free graph on n vertices,then for any vertex v and any two distinct vertices x and y in V(G)-{v},G has a path containing v and all neighbors of v and connecting x and y;2) Let C be the longest cycle in a 3-connected claw-free graph G and H a component of G-C,and if H is connected but not 2-connected,then there exist nonadjacent vertices u and v in H such that |V(C)|≥(3(d(u)+)d(v))-2. 展开更多
关键词 longest path cycle claw-free graph
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Individual tree extraction from terrestrial laser scanning data via graph pathing 认领 引用 被引量：2
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作者 Di Wang Xinlian Liang +1 位作者 Gislain II Mofack Olivier Martin-Ducup 《Forest Ecosystems》 SCIE CSCD 2021年第4期903-913,共11页
Background:Individual tree extraction from terrestrial laser scanning(TLS)data is a prerequisite for tree-scale estimations of forest biophysical properties.This task currently is undertaken through laborious and time... Background:Individual tree extraction from terrestrial laser scanning(TLS)data is a prerequisite for tree-scale estimations of forest biophysical properties.This task currently is undertaken through laborious and time-consuming manual assistance and quality control.This study presents a new fully automatic approach to extract single trees from large-area TLS data.This data-driven method operates exclusively on a point cloud graph by path finding,which makes our method computationally efficient and universally applicable to data from various forest types.Results:We demonstrated the proposed method on two openly available datasets.First,we achieved state-of-the-art performance on locating single trees on a benchmark dataset by significantly improving the mean accuracy by over 10% especially for difficult forest plots.Second,we successfully extracted 270 trees from one hectare temperate forest.Quantitative validation resulted in a mean Intersection over Union(mIoU)of 0.82 for single crown segmentation,which further led to a relative root mean square error(RMSE%)of 21.2% and 23.5% for crown area and tree volume estimations,respectively.Conclusions:Our method allows automated access to individual tree level information from TLS point clouds.The proposed method is free from restricted assumptions of forest types.It is also computationally efficient with an average processing time of several seconds for one million points.It is expected and hoped that our method would contribute to TLS-enabled wide-area forest qualifications,ranging from stand volume and carbon stocks modelling to derivation of tree functional traits as part of the global ecosystem understanding. 展开更多
关键词 Point cloud Segmentation Tree extraction Graph pathing
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Improving Centralized Path Calculation Based on Graph Compression 认领 引用 被引量：1
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作者 Zhenglian Li Lixin Ji +1 位作者 Ruiyang Huang Shuxin Liu 《China Communications》 SCIE CSCD 2018年第6期120-124,共5页
Shortest-path calculation on weighted graphs are an essential operation in computer networks. The performance of such algorithms has become a critical challenge in emerging software-defined networks(SDN),since SDN con... Shortest-path calculation on weighted graphs are an essential operation in computer networks. The performance of such algorithms has become a critical challenge in emerging software-defined networks(SDN),since SDN controllers need to centralizedly perform a shortest-path query for every flow,usually on large-scale network. Unfortunately,one of the challenges is that current algorithms will become incalculable as the network size increases. Therefore, inspired by the compression graph in the field of compute visualization,we propose an efficient shortest path algorithm by compressing the original big network graph into a small one, but the important graph properties used to calculate path is reserved. We implement a centralized version of our approach in SDN-enabled network,and the evaluations validate the improvement compared with the well-known algorithms. 展开更多
关键词 graph representation path compression shortest path
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Semantic-aware graph convolution network on multi-hop paths for link prediction 认领 引用 被引量：1
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作者 彭斐 CHEN Shudong +2 位作者 QI Donglin YU Yong TONG Da 《High Technology Letters》 EI CAS 2023年第3期269-278,共10页
Knowledge graph(KG) link prediction aims to address the problem of missing multiple valid triples in KGs. Existing approaches either struggle to efficiently model the message passing process of multi-hop paths or lack... Knowledge graph(KG) link prediction aims to address the problem of missing multiple valid triples in KGs. Existing approaches either struggle to efficiently model the message passing process of multi-hop paths or lack transparency of model prediction principles. In this paper,a new graph convolutional network path semantic-aware graph convolution network(PSGCN) is proposed to achieve modeling the semantic information of multi-hop paths. PSGCN first uses a random walk strategy to obtain all-hop paths in KGs,then captures the semantics of the paths by Word2Sec and long shortterm memory(LSTM) models,and finally converts them into a potential representation for the graph convolution network(GCN) messaging process. PSGCN combines path-based inference methods and graph neural networks to achieve better interpretability and scalability. In addition,to ensure the robustness of the model,the value of the path thresholdKis experimented on the FB15K-237 and WN18RR datasets,and the final results prove the effectiveness of the model. 展开更多
关键词 knowledge graph(KG) link prediction graph convolution network(GCN) knowledge graph completion(KGC) multi-hop paths semantic information
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Design of a sustainable development path in Chenzhou based on a knowledge graph 认领 引用
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作者 Qiuli Lv Lijie Gao +1 位作者 Longyu Shi Houbo Zhou 《Chinese Journal of Population,Resources and Environment》 2024年第4期455-468,共14页
Sustainable urban development involves many fields with complex data types and rich semantic relationships,such as the economic,societal,and ecological fields.Knowledge graphs provide a new means for sustainable urban... Sustainable urban development involves many fields with complex data types and rich semantic relationships,such as the economic,societal,and ecological fields.Knowledge graphs provide a new means for sustainable urban development research by leveraging their strengths in the construction of knowledge networks and display of knowledge associations.Focusing on Chenzhou,a resource-based city serving as a China’s Innovation Demonstration Zone for Sustainable Development Agenda,this study adopted a top-down approach,applying the“seven-step”and“skeleton”methods to construct an ontology for sustainable urban development through manual editing.A knowledge graph was constructed for Chenzhou’s sustainable development,comprising 515 nodes,3209 relations,and 28157 attributes.Sustainable measures and pathways were proposed based on this knowledge graph.The results showed that Chenzhou’s future sustainable development should focus on innovation,growth,emissions reduction,centering around high-quality and sustainable development.Promoting the transfer and transformation of scientific and technological achievements,accelerating the optimization and upgrading of industrial structures,and enhancing talent cultivation and recruitment will foster new quality productive forces,providing strong momentum and support for the high-quality and sustainable development of Chenzhou.To accelerate the green economy transition,Chenzhou should improve the market-oriented allocation system for resources and environmental factors,explore the“gross ecosystem product+eco environment-oriented development”project implementation model,encourage enterprises to adopt environmental,social,and governance principles,and foster synergies between supply and demand.Furthermore,coordinating Chenzhou’s low-carbon city pilot projects and constructing carbon sequestration pathways that leverage nature-based solutions will help implement the“dual carbon”actions and enhance the city’s ability to respond to climate change. 展开更多
关键词 Ontological modeling Knowledge graph Chenzhou Sustainable urban development Path design
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Path Cover in K1,4-Free Graphs 认领 引用
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作者 Mingda LIU Xiaodong CHEN Mingchu LI 《Journal of Mathematical Research with Applications》 CSCD 2019年第3期315-320,共6页
For a graph G, a path cover is a set of vertex disjoint paths covering all the vertices of G, and a path cover number of G, denoted by p(G), is the minimum number of paths in a path cover among all the path covers of ... For a graph G, a path cover is a set of vertex disjoint paths covering all the vertices of G, and a path cover number of G, denoted by p(G), is the minimum number of paths in a path cover among all the path covers of G. In this paper, we prove that if G is a K1,4-free graph of order n and σk+1(G) ≥ n-k, then p(G) ≤ k, where σk+1(G) = min{∑v∈S d(v) : S is an independent set of G with |S| = k + 1}. 展开更多
关键词 path cover path cover number K1,4-free graph non-insertable vertex
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On traceable iterated line graph and hamiltonian path index 认领 引用
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作者 NIU Zhao-hong XIONG Li-ming YANG Wei-hua 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2024年第2期239-252,共14页
Xiong and Liu[21]gave a characterization of the graphs G for which the n-iterated line graph Ln(G)is hamiltonian,for n≥2.In this paper,we study the existence of a hamiltonian path in Ln(G),and give a characteri... Xiong and Liu[21]gave a characterization of the graphs G for which the n-iterated line graph Ln(G)is hamiltonian,for n≥2.In this paper,we study the existence of a hamiltonian path in Ln(G),and give a characterization of G for which Ln(G)has a hamiltonian path.As applications,we use this characterization to give several upper bounds on the hamiltonian path index of a graph. 展开更多
关键词 iterated line graph traceable hamiltonian index hamiltonian path index
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The Path-Positive Property on the Products of Graphs 认领 引用
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作者 连广昌 《Journal of Southeast University(English Edition)》 CAS 1998年第2期130-134,共5页
The products of graphs discussed in this paper are the following four kinds: the Cartesian product of graphs, the tensor product of graphs, the lexicographic product of graphs and the strong direct product of graphs. ... The products of graphs discussed in this paper are the following four kinds: the Cartesian product of graphs, the tensor product of graphs, the lexicographic product of graphs and the strong direct product of graphs. It is proved that:① If the graphs G 1 and G 2 are the connected graphs, then the Cartesian product, the lexicographic product and the strong direct product in the products of graphs, are the path positive graphs. ② If the tensor product is a path positive graph if and only if the graph G 1 and G 2 are the connected graphs, and the graph G 1 or G 2 has an odd cycle and max{ λ 1μ 1,λ nμ m}≥2 in which λ 1 and λ n [ or μ 1 and μ m] are maximum and minimum characteristic values of graph G 1 [ or G 2 ], respectively. 展开更多
关键词 product of graphs path positive property Cartesian product of graphs tensor product of graphs lexicographic product of graphs strong direct product of graphs
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Outer-Independent Roman Domination on Cartesian Product of Paths 认领 引用
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作者 Junzhe GUO Hong GAO Yuansheng YANG 《Journal of Mathematical Research with Applications》 CSCD 2025年第1期11-19,共9页
Outer-independent Roman domination on graphs originates from the defensive strategy of Ancient Rome,which is that if any city without an army is attacked,a neighboring city with two armies could mobilize an army to su... Outer-independent Roman domination on graphs originates from the defensive strategy of Ancient Rome,which is that if any city without an army is attacked,a neighboring city with two armies could mobilize an army to support it and any two cities that have no army cannot be adjacent.The outer-independent Roman domination on graphs is an attractive topic in graph theory,and the definition is described as follows.Given a graph G=(V,E),a function f:V(G)→{0,1,2}is an outer-independent Roman dominating function(OIRDF)if f satisfies that every vertex v∈V with f(v)=0 has at least one adjacent vertex u∈N(v)with f(u)=2,where N(v)is the open neighborhood of v,and the set V0={v|f(v)=0}is an independent set.The weight of an OIRDF f is w(f)=∑v∈Vf(v).The value of minf w(f)is the outerindependent Roman domination number of G,denoted asγoiR(G).This paper is devoted to the study of the outer-independent Roman domination number of the Cartesian product of paths Pn□Pm.With the help of computer,we find some recursive OIRDFs and then we present an upper bound ofγoiR(Pn□Pm).Furthermore,we prove the lower bound ofγoiR(Pn□Pm)(n≤3)is equal to the upper bound.Hence,we achieve the exact value ofγoiR(Pn□Pm)for n≤3 and the upper bound ofγoiR(Pn□Pm)for n≥4. 展开更多
关键词 Roman domination outer-independent Roman domination Cartesian product graphs paths
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