Abstract: The total chromatic number X_T(G) of graph G is the least number of colors assigned to VE(G) such that no adjacent or incident elements receive the same color.Given graphs G₁,G₂, the join of G₁ and G₂, denoted by G₁∨G₂, is a graph G, V(G)=V(G₁)∪V(G₂) and E(G)=E(G₁)∪E(G₂) ∪{uv|u∈V(G₁), v ∈V(G₂)}. In this paper, it's proved that if v(G)=v(H), both G^c and H^c contain perfect matching and one of the followings holds:(i)Δ(G)=Δ(H) and there exist edge e∈ E(G), e'∈E(H) such that both G-e and H-e' are of Class l; (ii)Δ(G)<Δ(H) and there exixst an edge e ∈E(H) such that H-e is of Class 1, then, the total coloring conjecture is true for graph G ∨H.

Key words: graph, join of graphs, total chromatic number