### Total coloring conjecture on certain classes of product graphs

#### Abstract

*G*is an assignment of colors to the elements of the graph

*G*such that no adjacent vertices and edges receive the same color. The total chromatic number of a graph

*G*, denoted by

*χ*″(

*G*), is the minimum number of colors that suffice in a total coloring. Behzad and Vizing conjectured that for any graph

*G*,

*Δ*(

*G*)+1 ≤

*χ*″(

*G*)≤

*Δ*(

*G*)+2, where

*Δ*(

*G*) is the maximum degree of

*G*. In this paper, we prove the Behzad and Vizing conjecture for Indu - Bala product graph, Skew and Converse Skew product graph, Cover product graph, Clique cover product graph and Comb product graph.

#### Keywords

#### Full Text:

PDFDOI: http://dx.doi.org/10.5614/ejgta.2023.11.1.18

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