Abstract
The total coloring of a graph G is defined as assigning colors to the set of vertices and set of edges of G so that any adjacent or incident elements of G receive different colors. The least number of colors required to obtain a total coloring of G is the total chromatic number of G. The Total Coloring Conjecture by Behzad claims that ⍙(G) + 1 ≤ χ T (G) ≤ ⍙ (G) + 2. This paper studies the total chromatic number of Honeycomb network and the conjecture holds for the honeycomb network
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