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Hamiltonicity of Claw-free Graphs Involving Domination Number and Clique Covering 认领 引用
1
作者 WANG Lu XIONG Liming 《数学进展》 CSCD 北大核心 2026年第4期787-797,共11页
The closure of Gdenoted by cl(G),is obtained by recursively performing the local completion operation at eligible vertices as long as possible.The core of H is the graph co(H)obtained from H by deleting all the vertic... The closure of Gdenoted by cl(G),is obtained by recursively performing the local completion operation at eligible vertices as long as possible.The core of H is the graph co(H)obtained from H by deleting all the vertices of degree 1,and replacing the path xyz by the edge xz for each y of degree 2.In this paper,we discuss the Hamiltonicity of 3-connected claw-free graph under domination number and clique covering,and the Hamiltonicity of the 3-connected claw-free and hourglass-free graphs under domination number.We show that:(1)G is hamiltonian or cl(G)=L(H),and co(H)can be contracted to the Petersen graph if G is a 3-connected claw-free graph and thedomination number ofG is at most 6;(2)G is hamiltonian or cl(G)=L(H),where the reduction ofco(H)is a member of{P,P(14)},if G is a 3-connected claw-free,hourglass-free graph with domination number at most 11;(3)G is hamiltonian or cl(G)=L(H),and co(H)can becontracted to the Petersen graph,if G is a 3-connected claw-free graph with clique covering number at most 12. 展开更多
关键词 hamiltonian domination number claw-free clique covering number
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Outer-Independent Roman Domination on Cartesian Product of Paths 认领 引用
2
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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Perfect Double Roman Domination on Cographs 认领 引用
3
作者 LI Peng XUE Xin-yi +1 位作者 LONG Yang-jing LI Xue-bo 《Chinese Quarterly Journal of Mathematics》 2025年第2期158-168,共11页
Consider a graph G=(V,E).A perfect double Roman dominating function(PDRDF for short)is a function h:V→{0,1,2,3}that satisfies the condition∑y∈NG[x],h(y≥1)h(y)=|{y∈NG(x):h(y)≥1}|+2 for any x∈V with h(x)≤1.Th... Consider a graph G=(V,E).A perfect double Roman dominating function(PDRDF for short)is a function h:V→{0,1,2,3}that satisfies the condition∑y∈NG[x],h(y≥1)h(y)=|{y∈NG(x):h(y)≥1}|+2 for any x∈V with h(x)≤1.The weightω(h)of this function is∑y∈Vh(y).The perfect double Roman domination number(PDRD-number)of G,denoted byγdRp(G),is defined as the minimum weight among all PDRDFs of G.This article presents a comprehensive analysis of the PDRD-number of connected cographs,demonstrating that it falls within the set{2,3,4,5,6}.Furthermore,it establishes that for any integer i≥7,there is a connected cograph G such that its PDRD-number is equal to i. 展开更多
关键词 Cographs Double Roman domination Perfect double Roman domination
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A Bilinear Sparse Domination for the Maximal Calder´on Commutator with Rough Kernel 认领 引用
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作者 WANG Meizhong ZHAO Junyan 《数学进展》 CSCD 北大核心 2025年第5期1059-1074,共16页
LetΩbe homogeneous of degree zero,integrable on Sd−1 and have vanishing moment of order one,a be a function on Rd such that ∇a∈L∞(Rd).Let T*Ω,a be the maximaloperator associated with the d-dimensional... LetΩbe homogeneous of degree zero,integrable on Sd−1 and have vanishing moment of order one,a be a function on Rd such that ∇a∈L∞(Rd).Let T*Ω,a be the maximaloperator associated with the d-dimensional Calder´on commutator defined by T*Ωaf(x):=supε>0|∫|x-y|>ε^Ω(x-y)/|x-y|d+1(a(x)-a(y))f(y)dy.In this paper,the authors establish bilinear sparse domination for T*Ω,a under the assumption Ω∈L∞(Sd−1).As applications,some quantitative weighted bounds for T*Ω,a are obtained. 展开更多
关键词 Calderon commutator Fourier transform multiplier operator approximation bilinear sparse domination rough kernel
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A Game-Theoretic Approach to Solving the Roman Domination Problem 认领 引用
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作者 Xiuyang Chen Changbing Tang +1 位作者 Zhao Zhang Guanrong Chen 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2025年第5期1024-1040,共17页
The Roman domination problem is an important combinatorial optimization problem that is derived from an old story of defending the Roman Empire and now regains new significance in cyber space security,considering back... The Roman domination problem is an important combinatorial optimization problem that is derived from an old story of defending the Roman Empire and now regains new significance in cyber space security,considering backups in the face of a dynamic network security requirement.In this paper,firstly,we propose a Roman domination game(RDG)and prove that every Nash equilibrium(NE)of the game corresponds to a strong minimal Roman dominating function(S-RDF),as well as a Pareto-optimal solution.Secondly,we show that RDG is an exact potential game,which guarantees the existence of an NE.Thirdly,we design a game-based synchronous algorithm(GSA),which can be implemented distributively and converge to an NE in O(n)rounds,where n is the number of vertices.In GSA,all players make decisions depending on local information.Furthermore,we enhance GSA to be enhanced GSA(EGSA),which converges to a better NE in O(n2)rounds.Finally,we present numerical simulations to demonstrate that EGSA can obtain a better approximate solution in promising computation time compared with state-of-the-art algorithms. 展开更多
关键词 Distributed algorithm game theory multi-agent system potential game Roman dominating function
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On the Injective Equitable Domination of Graphs 认领 引用 被引量：1
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作者 Ahmad N. Alkenani Hanaa Alashwali Najat Muthana 《Applied Mathematics》 2016年第17期2132-2139,共8页
A dominating set D in a graph G is called an injective equitable dominating set (Inj-equitable dominating set) if for every , there exists such that u is adjacent to v and . The minimum cardinality of such a dominatin... A dominating set D in a graph G is called an injective equitable dominating set (Inj-equitable dominating set) if for every , there exists such that u is adjacent to v and . The minimum cardinality of such a dominating set is denoted by and is called the Inj-equitable domination number of G. In this paper, we introduce the injective equitable domination of a graph and study its relation with other domination parameters. The minimal injective equitable dominating set, the injective equitable independence number , and the injective equitable domatic number are defined. 展开更多
关键词 Domination Injective Equitable Domination Injective Equitable Domination Number
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Bounds of the Signed Edge Domination Number of Complete Multipartite Graphs 认领 引用 被引量：1
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作者 Yancai ZHAO 《Journal of Mathematical Research with Applications》 CSCD 2023年第2期161-165,共5页
A function f:E(G)→{−1,1}is called a signed edge dominating function(SEDF for short)of G if f[e]=f(N[e])=Σ_( e′∈N[e])f(e′)≥1,for every edge e∈E(G).w(f)=Σe∈E f(e)is called the weight of f.The signed edge dom... A function f:E(G)→{−1,1}is called a signed edge dominating function(SEDF for short)of G if f[e]=f(N[e])=Σ_( e′∈N[e])f(e′)≥1,for every edge e∈E(G).w(f)=Σe∈E f(e)is called the weight of f.The signed edge domination numberγs′(G)of G is the minimum weight among all signed edge dominating functions of G.In this paper,we initiate the study of this parameter for G a complete multipartite graph.We provide the lower and upper bounds ofγs′(G)for G a complete r-partite graph with r even and all parts equal. 展开更多
关键词 signed edge domination signed edge domination number complete multipartite graph
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An Upper Bound for Total Domination Number 认领 引用 被引量：1
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作者 孙良 《Journal of Beijing Institute of Technology》 EI CAS 1995年第2期114+111-113,共114页
Let G=(V, E) be a simple graph without an isolate. A subset T of V is a total dominating set of G if for any there exists at least one vertex such that .The total domination number γ1(G) of G is the minimum order of ... Let G=(V, E) be a simple graph without an isolate. A subset T of V is a total dominating set of G if for any there exists at least one vertex such that .The total domination number γ1(G) of G is the minimum order of a total dominating set of G. This paper proves that if G is a connected graph with n≥3 vertices and minimum degree at least two. 展开更多
关键词 graphs (mathematics) / domination total domination number
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On the Uphill Domination Polynomial of Graphs 认领 引用
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作者 Thekra Alsalomy Anwar Saleh +1 位作者 Najat Muthana Wafa Al Shammakh 《Journal of Applied Mathematics and Physics》 2020年第6期1168-1179,共12页
A path π = [v1, v2, …, vk] in a graph G = (V, E) is an uphill path if deg(vi) ≤ deg(vi+1) for every 1 ≤ i ≤ k. A subset S &#8838; V(G) is an uphill dominating set if every vertex vi &#8712; V(G) lies... A path π = [v1, v2, …, vk] in a graph G = (V, E) is an uphill path if deg(vi) ≤ deg(vi+1) for every 1 ≤ i ≤ k. A subset S &#8838; V(G) is an uphill dominating set if every vertex vi &#8712; V(G) lies on an uphill path originating from some vertex in S. The uphill domination number of G is denoted by &#947;up(G) and is the minimum cardinality of the uphill dominating set of G. In this paper, we introduce the uphill domination polynomial of a graph G. The uphill domination polynomial of a graph G of n vertices is the polynomial , where up(G, i) is the number of uphill dominating sets of size i in G, and &#947;up(G) is the uphill domination number of G, we compute the uphill domination polynomial and its roots for some families of standard graphs. Also, UP(G, x) for some graph operations is obtained. 展开更多
关键词 Domination Uphill Domination Uphill Domination Polynomial
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Signed Roman (Total) Domination Numbers of Complete Bipartite Graphs and Wheels 认领 引用 被引量：4
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作者 ZHAO YAN-CAI MIAO LIAN-YING Du Xian-kun 《Communications in Mathematical Research》 CSCD 2017年第4期318-326,共9页
A signed(res. signed total) Roman dominating function, SRDF(res.STRDF) for short, of a graph G =(V, E) is a function f : V → {-1, 1, 2} satisfying the conditions that(i)∑v∈N[v]f(v) ≥ 1(res.∑v∈N(v)f(v) ≥ 1) for ... A signed(res. signed total) Roman dominating function, SRDF(res.STRDF) for short, of a graph G =(V, E) is a function f : V → {-1, 1, 2} satisfying the conditions that(i)∑v∈N[v]f(v) ≥ 1(res.∑v∈N(v)f(v) ≥ 1) for any v ∈ V, where N [v] is the closed neighborhood and N(v) is the neighborhood of v, and(ii) every vertex v for which f(v) =-1 is adjacent to a vertex u for which f(u) = 2. The weight of a SRDF(res. STRDF) is the sum of its function values over all vertices.The signed(res. signed total) Roman domination number of G is the minimum weight among all signed(res. signed total) Roman dominating functions of G. In this paper,we compute the exact values of the signed(res. signed total) Roman domination numbers of complete bipartite graphs and wheels. 展开更多
关键词 signed Roman domination signed total Roman domination complete bipartite graph wheel
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Fractional Domination of the Cartesian Products in Graphs 认领 引用 被引量：3
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作者 Baogen XU 《Journal of Mathematical Research with Applications》 CSCD 2015年第3期279-284,共6页
Let G = （V,E） be a simple graph. For any real function g ： V →R and a subset S 包涵于V, we write g（S） = ∑v∈sg（v）. A function f ： V → [0,1] is said to be a fractional dominating function （FDF） of G if f（... Let G = （V,E） be a simple graph. For any real function g ： V →R and a subset S 包涵于V, we write g（S） = ∑v∈sg（v）. A function f ： V → [0,1] is said to be a fractional dominating function （FDF） of G if f（N[v]） ≥ 1 holds for every vertex v ∈ V（G）. The fractional domination number γf（G） of G is defined as γf（G） = min{f（V）｜f is an FDF of G }. The fractional total dominating function f is defined just as the fractional dominating function, the difference being that f（N（v）） ≥ 1 instead of f（N[v]）≥ 1. The fractional total domination number γ^0f（G） of G is analogous. In this note we give the exact values of γf（Cm× Pn） and γ^0f（Cm × Pn） for all integers m ≥ 3 and n ≥ 2. 展开更多
关键词 Cartesian products fractional domination number fractional total dominationnumber
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Signed total domination in nearly regular graphs 认领 引用 被引量：2
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作者 康丽英 单而芳 《Journal of Shanghai University(English Edition)》 2006年第1期4-8,共5页
A function f： V（ G）→{1,1} defined on the vertices of a graph G is a signed total dominating function （STDF） if the sum of its function values over any open neighborhood is at least one. An STDF f is minimal if t... A function f： V（ G）→{1,1} defined on the vertices of a graph G is a signed total dominating function （STDF） if the sum of its function values over any open neighborhood is at least one. An STDF f is minimal if there does not extst a STDF g： V（G）→{-1,1}, f≠g, for which g （ v ）≤f（ v ） for every v∈V（ G ）. The weight of a STDF is the sum of its function values over all vertices. The signed total domination number of G is the minimum weight of a STDF of G, while the upper signed domination number of G is the maximum weight of a minimal STDF of G, In this paper, we present sharp upper bounds on the upper signed total domination number of a nearly regular graph. 展开更多
关键词 signed total domination nearly regular graph bounds.
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Bounds on Fractional Domination of Some Products of Graphs 认领 引用
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作者 陈学刚 孙良 邢化明 《Journal of Beijing Institute of Technology》 EI CAS 2004年第1期90-93,共4页
Let γ f(G) and γ~t f(G) be the fractional domination number and fractional total domination number of a graph G respectively. Hare and Stewart gave some exact fractional domination number of P n×P m (grid graph... Let γ f(G) and γ~t f(G) be the fractional domination number and fractional total domination number of a graph G respectively. Hare and Stewart gave some exact fractional domination number of P n×P m (grid graph) with small n and m . But for large n and m , it is difficult to decide the exact fractional domination number. Motivated by this, nearly sharp upper and lower bounds are given to the fractional domination number of grid graphs. Furthermore, upper and lower bounds on the fractional total domination number of strong direct product of graphs are given. 展开更多
关键词 fractional domination number fractional total domination number grid graph strong direct product
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CONVEX CONCENTRATION INEQUALITIES FOR CONTINUOUS GAS AND STOCHASTIC DOMINATION 认领 引用 被引量：1
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作者 马宇韬 《Acta Mathematica Scientia》 SCIE 2009年第5期1461-1468,共8页
In this article, we consider the continuous gas in a bounded domain ∧ of R^＋ or R^d described by a Gibbsian probability measure μη∧ associated with a pair interaction φ, the inverse temperature β, the activity... In this article, we consider the continuous gas in a bounded domain ∧ of R^＋ or R^d described by a Gibbsian probability measure μη∧ associated with a pair interaction φ, the inverse temperature β, the activity z 〉 0, and the boundary condition η. Define F ∫ωf（s）wA（ds）. Applying the generalized Ito＇s formula for forward-backward martingales （see Klein et M. [5]）, we obtain convex concentration inequalities for F with respect to the Gibbs measure μη∧. On the other hand, by FKG inequality on the Poisson space, we also give a new simple argument for the stochastic domination for the Gibbs measure. 展开更多
关键词 continuous gas Gibbs measure convex concentration inequality Ito＇s formula stochastic domination
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关于图的积的Domination数 认领 引用 被引量：1
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作者 康丽英 单而芳 《应用数学》 北大核心 1996年第4期526-528,共3页
关于图的积的Domination数康丽英，单而芳（石家庄铁道学院基础部石家庄050043）（石家庄师专数学系石家庄050041）关键词：图；θ－图；Dominating集AMS（1991）主题分类：05C35．本文所讨论的图均为无环、无重边的有限简单...
关键词 图 Dominating集 积 Domination数 简单图
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Italian Domination of Strong Product of Two Paths 认领 引用
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作者 WEI Li-yang LI Feng 《Chinese Quarterly Journal of Mathematics》 2024年第3期221-234,共14页
The domination problem of graphs is an important issue in the field of graph theory.This paper mainly considers the Italian domination number of the strong product between two paths.By constructing recursive Italian d... The domination problem of graphs is an important issue in the field of graph theory.This paper mainly considers the Italian domination number of the strong product between two paths.By constructing recursive Italian dominating functions,the upper bound of its Italian domination number is obtained,and then a partition method is proposed to prove its lower bound.Finally,this paper yields a sharp bound for the Italian domination number of the strong product of paths. 展开更多
关键词 Partitioning approach Roman domination Italian domination Strong product
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The Generalization of Signed Domination Number of Two Classes of Graphs 认领 引用 被引量：1
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作者 Xia Hong Guoyan Ao Feng Gao 《Open Journal of Discrete Mathematics》 2021年第4期114-132,共19页
Let be a graph. A function is said to be a Signed Dominating Function (SDF) if holds for all . The signed domination number . In this paper, we determine the exact value of the Signed Domination Number of graphs and f... Let be a graph. A function is said to be a Signed Dominating Function (SDF) if holds for all . The signed domination number . In this paper, we determine the exact value of the Signed Domination Number of graphs and for , which is generalized the known results, respectively, where and are denotes the k-th power graphs of cycle and path . 展开更多
关键词 Signed Domination Function Signed Domination Numbers Graphs Cn style="margin-left:-7px ">k Graphs Pn style="margin-left:-7px ">k
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On the Total Domination Number of Graphs with Minimum Degree at Least Three 认领 引用
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作者 刘海龙 孙良 《Journal of Beijing Institute of Technology》 EI CAS 2002年第2期217-219,共3页
Let G be a simple graph with no isolated vertices. A set S of vertices of G is a total dominating set if every vertex of G is adjacent to some vertex in S . The total domination number of G , denoted by γ t (G) , is ... Let G be a simple graph with no isolated vertices. A set S of vertices of G is a total dominating set if every vertex of G is adjacent to some vertex in S . The total domination number of G , denoted by γ t (G) , is the minimum cardinality of a total dominating set of G . It is shown that if G is a graph of order n with minimum degree at least 3, then γ t (G)≤n/2 . Thus a conjecture of Favaron, Henning, Mynhart and Puech is settled in the affirmative. 展开更多
关键词 simple graph domination total domination
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Lower Bounds on the Majority Domination Number of Graphs 认领 引用
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作者 刘海龙 孙良 田贺民 《Journal of Beijing Institute of Technology》 EI CAS 2002年第4期436-438,共3页
Let G=(V,E) be a simple graph. For any real valued function f∶V→R and SV, let f(S)=∑ u∈S?f(u). A majority dominating function is a function f∶V→{-1,1} such that f(N)≥1 for at least half the vertices v∈V. Then ... Let G=(V,E) be a simple graph. For any real valued function f∶V→R and SV, let f(S)=∑ u∈S?f(u). A majority dominating function is a function f∶V→{-1,1} such that f(N)≥1 for at least half the vertices v∈V. Then majority domination number of a graph G is γ maj(G)=min{f(V)|f is a majority dominating function on G}. We obtain lower bounds on this parameter and generalize some results of Henning. 展开更多
关键词 dominating function signed domination number majority domination number
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Signed Total Domination in Graphs 认领 引用 被引量：4
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作者 邢化明 孙良 陈学刚 《Journal of Beijing Institute of Technology》 EI CAS 2003年第3期319-321,共3页
Let G=(V,E) be a simple graph. For any real valued function f:V →R, the weight of f is f(V) = ∑f(v) over all vertices v∈V . A signed total dominating function is a function f:V→{-1,1} such that f(N(v)) ≥1 for... Let G=(V,E) be a simple graph. For any real valued function f:V →R, the weight of f is f(V) = ∑f(v) over all vertices v∈V . A signed total dominating function is a function f:V→{-1,1} such that f(N(v)) ≥1 for every vertex v∈V . The signed total domination number of a graph G equals the minimum weight of a signed total dominating function on G . In this paper, some properties of the signed total domination number of a graph G are discussed. 展开更多
关键词 total dominating function signed total dominating function signed total domination number
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