Total chromatic number of one kind of join graphs

The total chromatic number χT(G)χT(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 χT(G)=Δ(G)+1χT(G)=Δ(G)+1. In this paper we prove that the join of a complete inequibipartite graph Kn1,n2Kn1,n2 and a path PmPm is of Type 1.