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 simple 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 tight bound of the total coloring conjecture for the three types of corona products (vertex, edge and neighborhood) of graphs.
R. Vignesh, Geetha, J., and Dr. Somasundaram K., “Total Coloring Conjecture for Vertex, Edge and Neighborhood Corona Products of Graphs”, Discrete Mathematics, Algorithms and Applications, vol. 11, no. 1, 2019.