Abstract
The total chromatic number, χ ″ ( G ) is the minimum number of colors which need to be assigned to obtain a total coloring of the graph G. The Total Coloring Conjecture (TCC) made independently by Behzad and Vizing that for any graph, χ ″ ( G ) ≤ Δ ( G ) + 2 , where Δ ( G ) represents the maximum degree of G. In this paper we obtained the total chromatic number for some classes of four regular circulant graphs.
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