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Publication Type : Journal Article
Publisher : Discrete Mathematics, Algorithms and Applications
Source : Discrete Mathematics, Algorithms and Applications, Volume 11, Number 01, p.1950014 (2019)
Url : https://doi.org/10.1142/S1793830919500149
Campus : Coimbatore
School : School of Engineering
Department : Mathematics
Year : 2019
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 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.
Cite this Research Publication : R. Vignesh, J. Geetha, and Dr. Somasundaram K., “Total coloring conjecture for vertex, edge and neighborhood corona products of graphs”, Discrete Mathematics, Algorithms and Applications, vol. 11, p. 1950014, 2019.