若干笛卡尔积图的点可区别全色数
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摘要
图的一个正常的全染色如果满足不同点的点及其关联边的色集合不同,则称该染色法为点可区别全染色,其所用最少颜色数称为该图的点可区别全色数.给出了星和星,星和扇,扇和扇,星和轮的笛卡尔积图的点可区别全色数.
A proper total-coloring is called vertex-distinguishing total-coloring if the color sets of different vertex and its incident edge are different.The minimum number of colors of a vertex-distinguishing total-coloring is called the vertex-distinguishing total chromatic numbers of the graph.In this paper,the vertex-distinguishing total chromatic numbers of Sm□Sn,Sm□Fnand Fm□Fnare given.
A proper total-coloring is called vertex-distinguishing total-coloring if the color sets of different vertex and its incident edge are different.The minimum number of colors of a vertex-distinguishing total-coloring is called the vertex-distinguishing total chromatic numbers of the graph.In this paper,the vertex-distinguishing total chromatic numbers of Sm□Sn,Sm□Fnand Fm□Fnare given.
引文
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[2]BALISTER P N,GYORI E,LEHEL J,et al.Adjacent vertex distinguishing Edge-colorings[J].J Graph Theory,2003,42:95-109.
[3]HATAMI H.Δ+300is a bound on the adjacent vertex distinguishing edge chromatic number[J].Journal of Combinatorial Theory,Series B,2005,95:246-256.
[4]ZHANG Zhong-fu,LIU Lin-zhong,WANG Jianfang.Adjacent strong edge coloring of graphs[J].Appl Math Lett,2002,15:623-626.
[5]张婷,李沐春,徐保根,等.关于Cm□C5n的全色数和邻强边色数[J].兰州交通大学学报,2007,26(6):124-126.
[6]张忠辅,李敬文,陈祥恩,等.图的距离不大于β的任意两点可区别的边染色[J].数学学报,2006,49(3):703-708.
[7]ZHANG Zhong-fu,QIU Peng-xiang,XU Bao-gen,et al.Vertex-distinguishing total coloring of graphs[J].Ars Comb,2008,87:33-45.
[8]张忠辅,李敬文,陈祥恩,等.图的距离不大于β的任意两点可区别的全染色[J].中国科学,2006,49(10):1430-1440.
[9]ZHANG Zhong-fu,LI Jing-wen,CHEN Xiang-en,et al.On adjacent vertex distinguishing total coloring of graphs[J].Sci China(Ser A),2005,48:289-299.
[10]BONDY J A,MURTY U S R.Graph Theory[M].New York:Springer,2008.
[2]BALISTER P N,GYORI E,LEHEL J,et al.Adjacent vertex distinguishing Edge-colorings[J].J Graph Theory,2003,42:95-109.
[3]HATAMI H.Δ+300is a bound on the adjacent vertex distinguishing edge chromatic number[J].Journal of Combinatorial Theory,Series B,2005,95:246-256.
[4]ZHANG Zhong-fu,LIU Lin-zhong,WANG Jianfang.Adjacent strong edge coloring of graphs[J].Appl Math Lett,2002,15:623-626.
[5]张婷,李沐春,徐保根,等.关于Cm□C5n的全色数和邻强边色数[J].兰州交通大学学报,2007,26(6):124-126.
[6]张忠辅,李敬文,陈祥恩,等.图的距离不大于β的任意两点可区别的边染色[J].数学学报,2006,49(3):703-708.
[7]ZHANG Zhong-fu,QIU Peng-xiang,XU Bao-gen,et al.Vertex-distinguishing total coloring of graphs[J].Ars Comb,2008,87:33-45.
[8]张忠辅,李敬文,陈祥恩,等.图的距离不大于β的任意两点可区别的全染色[J].中国科学,2006,49(10):1430-1440.
[9]ZHANG Zhong-fu,LI Jing-wen,CHEN Xiang-en,et al.On adjacent vertex distinguishing total coloring of graphs[J].Sci China(Ser A),2005,48:289-299.
[10]BONDY J A,MURTY U S R.Graph Theory[M].New York:Springer,2008.