Affiliation:
1. Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Coimbatore, India
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, [Formula: see text] is the minimum number of colors which need to be assigned to obtain a total coloring of the graph [Formula: see text]. The Total Coloring Conjecture made independently by Behzad and Vizing claims that, [Formula: see text], where [Formula: see text] represents the maximum degree of [Formula: see text]. 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.
Publisher
World Scientific Pub Co Pte Lt
Subject
Discrete Mathematics and Combinatorics
Cited by
3 articles.
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1. Total Chromatic Number for Certain Classes of Lexicographic Product Graphs;COMMUN COMB OPTIM;2024
2. Total chromatic number for certain classes of product graphs;Discrete Mathematics, Algorithms and Applications;2023-12-15
3. Total colorings-a survey;AKCE International Journal of Graphs and Combinatorics;2023-03-08