Total Chromatic Number of the Join of Km,n and Cn

Chinese Quarterly Journal of Mathematics ›› 2006, Vol. 21 ›› Issue (2): 264-270.

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.

Abstract

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

CLC Number:

O157.5

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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Total Chromatic Number of the Join of K_m,nand C_n

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