两类联的全色数

Total Chromatic Number of Two Kinds of Joins

图G的全色数χT(G)是使得V(G)∪E(G)中相邻或相关联的元素均染不同颜色的最少数目.如果χT(G)=Δ(G)+1,则称G是1-型的.证明了在m≠n1+2时非等部完全偶图Kn1,n2(n1<n2)和圈Cm的联是1-型的;在m=n且m是奇数时,Cm和Cn的联是2-型的.

The total chromatic number χ_T(G) of a graph G is the minimum number of colours need to colour the vertices and the edges of G such that no adjacent or incident pair of elements receive the same colour. G is called Type 1 if χ_T(G)= Δ(G)+1. In this paper we prove that if m≠n_1+2, then K_ n_1,n_2+C_n∈C^1_T and if m=n and m is odd, then C_m+C_n∈C^1_T.