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折叠立方体图的邻点可区别全色数

         

摘要

A total coloring of a simple graph G is a coloring of both edges and vertices. A total coloring is proper if no two adjacent or incident elements receive the same color. An adjacent vertex-distinguishing total coloring h of a simple graph G = (Y,E) is a proper total coloring of G such that H(u)≠ H(v) for any two adjacent vertices u and v, where H(u) = {h(u)} U) (h(uw)|uw ∈ E(G)} and H(v) = {h(v)} U {h(vx)[vx ∈ E(G)}. The minimum number of colors required for an adjacent vertex-distinguishing total coloring of G is called the adjacent vertex- distinguishing total chromatic number of G and denoted by Xat(G). In this paper, we consider the adjacent vertex-distinguishing total chromatic number of the folded hypercubes FQn and prove that Xat(FQn) = n + 3 for n ≥ 2.%简单图G的全染色是指对G的点和边都进行染色.称全染色为正常的如果没有相邻或关联元素染同一种颜色.简单图G=(VE)的正常全染色^称为它的邻点可区别全染色如果对任意两个相邻顶点u、v,有H(u)≠H(v),其中H(u)={(u))U{^(uw)|uw∈E(G))而H(v)={h(u)}U{h(vx)|vx∈E(G)).G的邻点可区别全染色所需最少颜色数称为G邻点可区别全色数,记为Xat(G).本文考虑折叠立方体图FQn的邻点可区别全色数,证明了对任意n≥2,有Xat(FQn)=n+3.

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