Total coloring conjecture on certain classes of product graphs - Kanagasabapathi Somasundaram; Jayabalan Geetha; Radhakrishnan Vignesh (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2023)
A total coloring of a graph 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.