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Algorithms 2018, 11(10), 161; https://doi.org/10.3390/a11100161

Total Coloring Conjecture for Certain Classes of Graphs

Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Coimbatore 641112, India
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Received: 30 August 2018 / Revised: 25 September 2018 / Accepted: 17 October 2018 / Published: 19 October 2018
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Abstract

A total coloring of a graph G is an assignment of colors to the elements of the graph G such that no two adjacent or incident elements 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 total coloring conjecture for certain classes of graphs of deleted lexicographic product, line graph and double graph. View Full-Text
Keywords: total coloring; lexicographic product; deleted lexicographic product; line graph; double graph total coloring; lexicographic product; deleted lexicographic product; line graph; double graph
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Vignesh, R.; Geetha, J.; Somasundaram, K. Total Coloring Conjecture for Certain Classes of Graphs. Algorithms 2018, 11, 161.

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