Algorithm on the Optimal Vertex-Distinguishing Total Coloring of mC9  

mC9的点可区别全染色的最优算法（英文）

作　　者：HE Yu-ping CHEN Xiang'en 何玉萍;陈祥恩(College of Mathematics and Statistics, Northwest Normal University)

机构地区：[1]College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,P.R.China

出　　处：《Chinese Quarterly Journal of Mathematics》2019年第3期242-258,共17页数学季刊（英文版）

基　　金：Supported by the NNSF of China(Grant No.11761064,61163037)

摘　　要：Let G be a simple graph and f be a proper total coloring(or a total coloring in brief) of G. For any vertex u in G, Cf(u) denote the set of colors of vertex u and edges which incident with vertex u. Cf(u) is said to be the color set of vertex u under f. If Cf(u) = Cf(v)for any two distinct vertices u and v of G, then f is called vertex-distinguishing total coloring of G(in brief VDTC), a vertex distinguishing total coloring using k colors is called k-vertexdistinguishing total coloring of G(in brief k-VDTC). The minimum number k for which there exists a k-vertex-distinguishing total coloring of G is called the vertex-distinguishing total chromatic number of G, denoted by χvt(G). By the method of prior distributing the color sets, we obtain vertex-distinguishing total chromatic number of m C9 in this paper.

关 键 词：the UNION of GRAPHS PROPER TOTAL COLORING vertex-distinguishing TOTAL COLORING vertex-distinguishing TOTAL CHROMATIC number 

分 类 号：O157.5[理学—数学]