TOTAL COLORINGS OF GRAPHS OF ORDER 2N HAVING MAXIMUM DEGREE 2N-2

Abstract

Let chi(t)(G) and DELTA(G) denote respectively the total chromatic number and maximum degree of graph G. Yap, Wang and Zhang proved in 1989 that if G is a graph of order p having DELTA(G) greater-than-or-equal-to p - 4, then chi(t)(G) less-than-or-equal-to DELTA(G) + 2. Hilton has characterized the class of graph G of order 2n having DELTA(G) = 2n - 1 such that chi(t)(G) = DELTA(G) + 2. In this paper, we charactarize the class of graphs G of order 2n having DELTA(G) = 2n - 2 such that chi(t)(G) = DELTA(G) + 2.