Publication Type : Journal Article
Source : Electronic Journal of Graph Theory and Applications, accepted, 2023.
Url : https://www.ejgta.org/index.php/ejgta/article/view/771
Campus : Coimbatore
School : School of Engineering
Department : Mathematics
Verified : No
Year : 2023
Abstract : 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.
Cite this Research Publication : R.Vignesh, J. Geetha and K. Somasundaram, Total Coloring Conjecture on Certain Classes of Product Graphs, Electronic Journal of Graph Theory and Applications, accepted, 2023.