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Product Cordial Graph in the Context of Some Graph Operations on Gear Graph 认领 引用 被引量：1
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作者 Udayan M. Prajapati Karishma K. Raval 《Open Journal of Discrete Mathematics》 2016年第4期259-267,共9页
A graph is said to be a product cordial graph if there exists a function with each edge assign the label , such that the number of vertices with label 0 and the number of vertices with label 1 differ atmost by 1, and ... A graph is said to be a product cordial graph if there exists a function with each edge assign the label , such that the number of vertices with label 0 and the number of vertices with label 1 differ atmost by 1, and the number of edges with label 0 and the number of edges with label 1 differ by atmost 1. We discuss the product cordial labeling of the graphs obtained by duplication of some graph elements of gear graph. Also, we derive some product cordial graphs obtained by vertex switching operation on gear graph. 展开更多
关键词 Product Cordial Labeling Gear Graph Duplication Vertex Switching
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Some Edge Product Cordial Graphs in the Context of Duplication of Some Graph Elements 认领 引用
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作者 Udayan M. Prajapati Prakruti D. Shah 《Open Journal of Discrete Mathematics》 2016年第4期248-258,共11页
For a graph, a function is called an edge product cordial labeling of G, if the induced vertex labeling function is defined by the product of the labels of the incident edges as such that the number of edges with labe... For a graph, a function is called an edge product cordial labeling of G, if the induced vertex labeling function is defined by the product of the labels of the incident edges as such that the number of edges with label 1 and the number of edges with label 0 differ by at most 1 and the number of vertices with label 1 and the number of vertices with label 0 differ by at most 1. In this paper, we show that the graphs obtained by duplication of a vertex, duplication of a vertex by an edge or duplication of an edge by a vertex in a crown graph are edge product cordial. Moreover, we show that the graph obtained by duplication of each of the vertices of degree three by an edge in a gear graph is edge product cordial. We also show that the graph obtained by duplication of each of the pendent vertices by a new vertex in a helm graph is edge product cordial. 展开更多
关键词 Graph Labeling Edge Product Cordial Labeling Duplication of a Vertex
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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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The Cordiality on the Union of 3-regular Connected Graph and Cycle 认领 引用 被引量：3
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作者 XIE Yan-tao CHE Ying-tao LIU Zhi-shan 《Chinese Quarterly Journal of Mathematics》 2010年第2期244-248,共5页
Diab proved the following graphs are Cordial;Pm K1,n if and only if(m,n) =(1,2);Cm K1,n;Pm Kn;Cm Kn for all m and n except m ≡ 2(mod 4).In this paper,we proved the Cordiality on the union of 3-regular connected graph... Diab proved the following graphs are Cordial;Pm K1,n if and only if(m,n) =(1,2);Cm K1,n;Pm Kn;Cm Kn for all m and n except m ≡ 2(mod 4).In this paper,we proved the Cordiality on the union of 3-regular connected graph K3 and cycle Cm.First we have the Lemma 2,if uv ∈ E(G),G is Cordial,we add 4 vertices x,y,z,w in sequence to the edge uv,obtain a new graph denoted by G*,then G* is still Cordial,by this lemma,we consider four cases on the union of 3-regular connected graph R3,and for every case we distinguish four subcases on the cycle Cm. 展开更多
关键词 3-regular graph Cordial graph union graph
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Cordial Labeling of Corona Product of Path Graph and Second Power of Fan Graph 认领 引用
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作者 Ashraf Ibrahim Hefnawy Elrokh Shokry Ibrahim Mohamed Nada Eman Mohamed El-Sayed El-Shafey 《Open Journal of Discrete Mathematics》 2021年第2期31-42,共12页
A graph is said to be cordial if it has 0 - 1 labeling which satisfies particular conditions. In this paper, we construct the corona between paths and second power of fan graphs and explain the necessary and sufficien... A graph is said to be cordial if it has 0 - 1 labeling which satisfies particular conditions. In this paper, we construct the corona between paths and second power of fan graphs and explain the necessary and sufficient conditions for this construction to be cordial. 展开更多
关键词 Corona Second Power of Fan Cordial Graph
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Tribonacci Cordial Labeling of Graphs 认领 引用
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作者 Sarbari Mitra Soumya Bhoumik 《Journal of Applied Mathematics and Physics》 2022年第4期1394-1402,共9页
We introduce Tribonacci cordial labeling as an extension of Fibonacci cordial labeling, a well-known form of vertex-labelings. A graph that admits Tribonacci cordial labeling is called Tribonacci cordial graph. In thi... We introduce Tribonacci cordial labeling as an extension of Fibonacci cordial labeling, a well-known form of vertex-labelings. A graph that admits Tribonacci cordial labeling is called Tribonacci cordial graph. In this paper we investigate whether some well-known graphs are Tribonacci cordial. 展开更多
关键词 Tribonacci Cordial Generalized Friendship Graph Wheel Graph Ring Sum Joint Sum
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Edge Product Cordial Labeling of Some Cycle Related Graphs 认领 引用
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作者 Udayan M. Prajapati Nittal B. Patel 《Open Journal of Discrete Mathematics》 2016年第4期268-278,共11页
For a graph having no isolated vertex, a function is called an edge product cordial labeling of graph G, if the induced vertex labeling function defined by the product of labels of incident edges to each vertex is suc... For a graph having no isolated vertex, a function is called an edge product cordial labeling of graph G, if the induced vertex labeling function defined by the product of labels of incident edges to each vertex is such that the number of edges with label 0 and the number of edges with label 1 differ by at most 1 and the number of vertices with label 0 and the number of vertices with label 1 also differ by at most 1. In this paper, we discuss edge product cordial labeling for some cycle related graphs. 展开更多
关键词 Graph Labeling Edge Product Cordial Labeling
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关于一点联的Cordial性的一个结果的推广 认领 引用 被引量：2
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作者 倪臣敏 刘峙山 陈丽娜 《延边大学学报（自然科学版）》 CAS 2007年第2期94-97,共4页
将文献[2](Shee S C,Ho Y S.The Cordiality of One-point Union of n-copies of a Graph.Discrete Math,1993,117:225-243)的结果推广到一般的圈的一点联,即粘连的圈的个数是任意的且每个圈的顶点数也是任意的情况,并给出了此类一点联... 将文献[2](Shee S C,Ho Y S.The Cordiality of One-point Union of n-copies of a Graph.Discrete Math,1993,117:225-243)的结果推广到一般的圈的一点联,即粘连的圈的个数是任意的且每个圈的顶点数也是任意的情况,并给出了此类一点联的Cordial性的分析证明. 展开更多
关键词 Cordial图 圈 一点联
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轮族的cordial性问题 认领 引用 被引量：7
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作者 堵根民 《内蒙古师范大学学报（自然科学汉文版）》 2008年第2期180-181,184,共2页
运用递推与扩展的方法,研究了轮族的cordial性问题,给出轮族sum from i=1 to n (W(ki))为非cordial图的充分必要条件:n为奇数且ki≡0(mod4)(i=1,2,…,n),或ki≡3(mod4)(i=1,2,…,n).
关键词 cordial图 cordial标号 轮族
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二部完全图为H_2-cordial图的充分必要条件 认领 引用 被引量：1
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作者 堵根民 《宁夏大学学报（自然科学版中英文）》 CAS 北大核心 2008年第4期309-310,313,共2页
在图的Hp-cordial系列问题中,有关H-cordial的讨论较多,而图的H2-cordial性结果,目前仅涉及完全图与轮.为此,在引入二部完全图的边标号矩阵表示法后,给出了二部完全图是H2-cordial图的充分必要条件.
关键词 二部完全图 矩阵表示法 H2-cordial
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几种特殊图之间和的Cordial性 认领 引用
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作者 连博勇 刘峙山 《延边大学学报（自然科学版）》 CAS 2009年第1期12-14,共3页
给出了路Pm、圈Cn、扇Fp和轮Wq4种图之间和的Cordial性,所得结果扩展了文献[1](Gallian J A.ADynamic Survey of Graph Labellings of Graphs.Electronic Journal of Combinatorics,2005(5):DS6)的研究工作.
关键词 Cordial图 图的和 路 圈 扇 轮
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两类H-cordial图的构造(英文) 认领 引用
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作者 倪臣敏 刘峙山 《延边大学学报（自然科学版）》 CAS 2008年第4期244-245,共2页
给出了图G是H-cordial图的一个必要条件,证明了基于两个正则图而构造的新图G*是H-cordial图,从而得到了两大类H-cordial图的构造方法,由此可推导出一系列图都是H-cordial图.
关键词 H-cordial图 k-正则图 Euler图
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与C(2m,2)有关图的Cordial性 认领 引用
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作者 任俊峰 王萍 《西昌学院学报（自然科学版）》 2012年第2期31-33,36,共3页
根据cordial图的定义,研究了C(2m,2),C(2m,2)+G,以及C(2m,2)×Pn的Cordial性,并给出了相应的Cordial标号。
关键词 Cordial图 Cordial标号 循环图 路 笛卡尔积
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K_m×P2n的Cordial性 认领 引用
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作者 任俊峰 宋晓刚 《西昌学院学报（自然科学版）》 2012年第1期55-56,62,共2页
由K_m×P_n(m=1,2,3,4)的cordial性,给出了K_M×P2n的Cordial标号,证明了这一类图是Cordial图。
关键词 Cordial图 Cordial标号 完全图 路 笛卡尔积
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基于邻接矩阵判断图的Cordial性 认领 引用
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作者 卞洪亚 《常熟理工学院学报》 2016年第2期96-99,共4页
给出了图G是Cordial图的充分必要条件;对于给定任意n阶图,给出如何利用计算机判断其Cordial性;利用计算机,给出找出所有n阶可Cordial图的方法.
关键词 Cordial图 邻接矩阵 简单图
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2-正则图的cordial性 认领 引用 被引量：5
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作者 徐丽平 刘峙山 倪臣敏 《延边大学学报（自然科学版）》 CAS 2008年第1期21-22,共2页
研究2-正则图G的cordial性,证明了2-正则图G是cordial图的充要条件为|G|≠2(mod4);取消了文献[1](Cahit I.On cordial and 3-equitbale labeling of graphs.Utilitas Math,1990,37:189-198)中具有4n+2条边的Euler图不是cordial图这一定... 研究2-正则图G的cordial性,证明了2-正则图G是cordial图的充要条件为|G|≠2(mod4);取消了文献[1](Cahit I.On cordial and 3-equitbale labeling of graphs.Utilitas Math,1990,37:189-198)中具有4n+2条边的Euler图不是cordial图这一定理中连通性条件,证明了具有4n+2条边并且顶点的度都是偶数的图不是cordial图. 展开更多
关键词 cordial标号 2-正则图 cordial图
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from i=1 to r (P_m_i×P_n_i)的cordial性 认领 引用 被引量：3
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作者 马黎政 刘峙山 陈丽娜 《延边大学学报（自然科学版）》 CAS 2008年第2期99-101,共3页
基于图的cordial标号,给出了3个引理:cordial图G联结上一个P2×Pn图得到的新图仍是cordial图;每个图P2k+1×P2l都有2个cordial标号;至少有1个图边数为偶数或者边数都为奇数但0边之和等于1边之和的2个cordial图的并为cordial图.... 基于图的cordial标号,给出了3个引理:cordial图G联结上一个P2×Pn图得到的新图仍是cordial图;每个图P2k+1×P2l都有2个cordial标号;至少有1个图边数为偶数或者边数都为奇数但0边之和等于1边之和的2个cordial图的并为cordial图.最后运用这3个引理证明了from i=1 to r (Pmi×Pni为cordial图. 展开更多
关键词 cordial图 路 笛卡尔积
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林的Cordial性 认领 引用 被引量：4
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作者 曹向东 刘峙山 《数学研究》 2008年第2期220-222,共3页
给出林是Cordial图的充要条件是它不是4k+2个奇度树的并.
关键词 Cordial图 林
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关于一些图的T_n-union的Cordial性 认领 引用 被引量：1
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作者 吴海平 刘峙山 《延边大学学报（自然科学版）》 CAS 2009年第4期312-314,共3页
将文献[5](Shee S C,Ho YS.The Cordiality of the Path-union ofnCopies of a Graph.Discrete Math,1996,151:221-229.)的结果推广到Tn-union的情形,且不要求每个节点的图形必须相同.并给出了任意圈和扇Tn-union的Cordial性的分析和证明.
关键词 Cordial图 Tn-union 圈 扇
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(Pm_1×Pn_1∨(Pm_2×Pn_2)和(P_m×P_n)∨C_k的Cordial性 认领 引用 被引量：1
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作者 刘庆 刘峙山 《延边大学学报（自然科学版）》 CAS 2009年第3期217-218,234,共2页
利用文献[5](Seoud M,Abdel Maqsoud A E I,Sheehan J.Harmonious Graphs.Util Math,1995,47:225-233.)中的引理1,研究了Pm1×Pn1与Pm2×Pn2的连接和Pm×Pn与Ck的连接的Cordial性,得到当m1,m2,n1,n2≥2时,(Pm1×Pn1)∨(... 利用文献[5](Seoud M,Abdel Maqsoud A E I,Sheehan J.Harmonious Graphs.Util Math,1995,47:225-233.)中的引理1,研究了Pm1×Pn1与Pm2×Pn2的连接和Pm×Pn与Ck的连接的Cordial性,得到当m1,m2,n1,n2≥2时,(Pm1×Pn1)∨(Pm2×Pn2)均为Cordial图;当m,n≥2时,(Pm×Pn)∨Ck是Cordial图的充要条件. 展开更多
关键词 Cordial图 笛卡尔积 连接
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