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Publication Type : Journal Article
Publisher : World Scientific Publishing Company
Source : Discrete Mathematics, Algorithms and Applications, 2023, DOI: https://doi.org/10.1142/S1793830923500994
Url : https://www.worldscientific.com/doi/abs/10.1142/S1793830923500994
Campus : Coimbatore
School : School of Engineering, School of Physical Sciences
Department : Mathematics
Year : 2023
Abstract : Total coloring is a function that assigns colors to the vertices and edges of the graph such that the adjacent and the incident elements receive different colors. The minimum number of colors required for a proper total coloring of a graph G is called the total chromatic number of G and is denoted by χ′′(G). Behzad–Vizing conjecture (Total Coloring Conjecture) states that for any graph G, χ′′(G)≤Δ(G)+2, where Δ(G) is the maximum degree of G. In this paper, we verify the Behzad–Vizing conjecture for some product graphs.
Cite this Research Publication : TP Sandhiya, J Geetha, K Somasundaram,"Total chromatic number for certain classes of product graphs," Discrete Mathematics, Algorithms and Applications, 2023, DOI: https://doi.org/10.1142/S1793830923500994