Publication Type : Journal Article
Source : Discrete Mathematics, Algorithms and Applications, Vol. 14, No. 03, 2150129 (2022), DOI: https://doi.org/10.1142/S1793830921501299
Url : https://www.worldscientific.com/doi/abs/10.1142/S1793830921501299
Keywords : Total coloring, lexicographic product, deleted lexicographic product
Campus : Coimbatore
School : School of Engineering
Department : Mathematics
Year : 2022
Abstract : A total coloring of a graph G is an assignment of colors to all the elements (vertices and edges) of the graph in such a way that no two adjacent or incident elements receive the same color. The Total Chromatic Number, χ′′(G) is the minimum number of colors which need to be assigned to obtain a total coloring of the graph G. The Total Coloring Conjecture made independently by Behzad and Vizing claims that, Δ(G)+1≤χ′′(G)≤Δ(G)+2, where Δ(G) represents the maximum degree of G. The lower bound is sharp, the upper bound remains to be proved. In this paper, we prove the Total Coloring Conjecture for certain classes of lexicographic product and deleted lexicographic product of graphs.
Cite this Research Publication : T. P. Sandhiya , J. Geetha and K. Somasundaram, "Total colorings of certain classes of lexicographic product graphs," Discrete Mathematics, Algorithms and Applications, Vol. 14, No. 03, 2150129 (2022), DOI: https://doi.org/10.1142/S1793830921501299