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.
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.
出处
《内江师范学院学报》
2012年第4期24-26,共3页
Journal of Neijiang Normal University
基金
宿州学院一般科研项目(2011yyb01)
