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
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
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
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
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.
文摘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.
文摘研究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.
文摘将文献[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.
文摘利用文献[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.
文摘给出了路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.
