关于图邻点可区别上界的一点注

摘要

A proper total coloring of simple connected graph G is called adjacent vertex-distinguishing total coloring if for any two adjacent vertices U and v in G,the set of colors assigned to u and to the edges incident to u differs from the set of colors assigned to v and to the edges incident to v.If the number of colors needed by a adjacent vertex distinguishing total coloring f is k,then f is called a k-adjacent vertex-distinguishing total coloring(k-AVDTC in brief).The number min{k|G has a k-AVDTC} is called adjacent vertex-distinguishing total-chromatic number of G and is denoted by χ′at(G).A upper bound of adjacent vertex distinguishing total chromatic number of graphs is presented.%设G为一简单连通图.它的一个正常全染色叫做一个邻点可区别的全染色.如果满足:对G的任意两个顶点u,v,都有染点u以及与u相连的边所形成的色集与染点v以及与v相连的边所形成的色集不同.如果一个邻点可区别的全染色需要的色数为κ,则把这个染色叫做k-邻点可区别的全染色(简记为k-AVDTC).对图G,记χ′at(G)=min{k|G有一个k-AVDTC},称χ′at(G)为图G的邻点可区别的全色数.本文给出了邻点可区别的全色数的一个上界.