Abstract
Let ? t (G) and ?(G) denote respectively the total chromatic number and maximum degree of graphG. Yap, Wang and Zhang proved in 1989 that ifG is a graph of orderp having ?(G)?p?4, then ? t (G≤Δ(G)+2. Hilton has characterized the class of graphG of order 2n having ?(G)=2n?1 such that ? t (G=Δ(G)+2. In this paper, we characterize the class of graphsG of order 2n having ?(G)=2n?2 such that ? t (G=Δ(G)+2
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