Km,n 和Cn的联图的全色数

数学季刊 ›› 2006, Vol. 21 ›› Issue (2): 264-270.

K_m,n和C_n的联图的全色数

College of Information Engineering, Information Engineering Institute, Zhengzhou 450002, China

收稿日期:2004-12-25 出版日期:2006-06-30 发布日期:2023-12-08
作者简介:LI Guang-rong(1981-),female,native of Zhoukou,Henan,engages in graph theory.

Total Chromatic Number of the Join of K_m,nand C_n

College of Information Engineering, Information Engineering Institute, Zhengzhou 450002, China

Received:2004-12-25 Online:2006-06-30 Published:2023-12-08
About author:LI Guang-rong(1981-),female,native of Zhoukou,Henan,engages in graph theory.

摘要/Abstract

摘要： The total chromatic number XT(G) of a graph G is the minimum number of colors needed to color the elements (vertices and edges) of G such that no adjacent or incident pair of elements receive the same color. G is called Type 1 if XT(G)=Δ(G) + 1. In this paper we prove that the join of a complete bipartite graph K_m,n and a cycle C_n is of Type 1.

关键词: total coloring, total chromatic number, join graphs, cycle, complete bipartite graph

Abstract: The total chromatic number XT(G) of a graph G is the minimum number of colors needed to color the elements (vertices and edges) of G such that no adjacent or incident pair of elements receive the same color. G is called Type 1 if XT(G)=Δ(G) + 1. In this paper we prove that the join of a complete bipartite graph K_m,n and a cycle C_n is of Type 1.

Key words: total coloring, total chromatic number, join graphs, cycle, complete bipartite graph

中图分类号:

O157.5

李光荣, 张利民. K_m,n和C_n的联图的全色数[J]. 数学季刊, 2006, 21(2): 264-270.

LI Guang-rong, ZHANG Li-min. Total Chromatic Number of the Join of K_m,nand C_n[J]. Chinese Quarterly Journal of Mathematics, 2006, 21(2): 264-270.

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