On the total coloring of graph G boolean OR H

The total chromatic number (chi 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 G(1), G(2), the join of G(1) and G(2), denoted by G(1) boolean OR G(2), is a graph G, V(G) = V(G(1))boolean OR V(G(2)) and E(G) = E(G(1))boolean OR E(G(2))boolean OR{uv \ u is an element of V(G(1)), v is an element of V(G(2))}. 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) Delta(G) = Delta(H) and there exist edge e is an element of E (H) such that both G - e and H - e' are of Class 1; (ii) Delta(G) < Delta(H) and there exist an edge e is an element of E(H) such that H - e is of Class 1, then, the total coloring conjecture is true for graph G boolean OR H.