| 关于双图的群染色（英文） |
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| 引用本文： | 杨星星.关于双图的群染色（英文）[J].内江师范学院学报,2012,27(4):24-26. |
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| 作者姓名： | 杨星星 |
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| 作者单位： | 宿州学院数学与统计学院,安徽宿州,234000 |
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| 摘 要： | 若图G=（V,E）,给定方向为D,A表示一个非平凡的阿贝尔群,F（G,A）表示映射f：E（G）→A的集合.若对任意f∈F（G,A）存在映射c：V（G）→A,使得G中的每一条有向边e=uv∈E（G）（方向是u→v）满足c（u）-c（v）≠f（e）,这时说图G是A-可染的.使得图G在方向D下是A-可染的,A的最小阶数为图G的群色数,记为χg（G）.主要是在分析了一些双图的特性的基础上讨论了它们的群色数.对于任意阶路的双图可得出其群色数都是3,还证明了圈的双图的群色数不超过5以及得到其它一些双图的群色数的上界.
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| 关 键 词： | group coloring group chromatic number double graphs |
On the Group Coloring of Some Double Graphs |
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| YANG Xing-xing.On the Group Coloring of Some Double Graphs[J].Journal of Neijiang Teachers College,2012,27(4):24-26. |
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| Authors: | YANG Xing-xing |
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| Institution: | YANG Xing-xing (School of Mathematics and Statistics,Suzhou University,Suzhou 234000,China) |
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| Abstract: | Let G be a graph and A an abelian group;Denote by F(G,A) the set of all functions from E(G) to A.Denote by D an orientation of E(G).For f∈F(G,A),an(A,f)-coloring of G under the orientation D is a function C:V(G)→A such that for every directed edge uv from u to v,c(u)-c(v)≠f(uv).G is A-colorable under the orientation D,if for any function f∈F(G,A),G has an(A,f)-coloring.The group chromatic number χg(G) of a graph G is the minimum number m such that G is A-coloring for any Abelian group A of order ≥m under the orientation D.In this paper,the author discussed the group coloring of some kinds of double graphs based on the analysis of their traits.Let G be a path,we proved that the group chromatic mumber of double path is 3 and also proved the group chromatic number of double cycle is at most 5,among other things. |
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| Keywords: | group coloring group chromatic number double graphs |
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