Total Coloring Conjecture for Certain Classes of Graphs
Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Coimbatore 641112, India
Author to whom correspondence should be addressed.
Received: 30 August 2018 / Revised: 25 September 2018 / Accepted: 17 October 2018 / Published: 19 October 2018
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
, is the minimum number of colors that suffice in a total coloring. Behzad and Vizing conjectured that for any graph 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.
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MDPI and ACS Style
Vignesh, R.; Geetha, J.; Somasundaram, K. Total Coloring Conjecture for Certain Classes of Graphs. Algorithms 2018, 11, 161.
Vignesh R, Geetha J, Somasundaram K. Total Coloring Conjecture for Certain Classes of Graphs. Algorithms. 2018; 11(10):161.
Vignesh, R.; Geetha, J.; Somasundaram, K. 2018. "Total Coloring Conjecture for Certain Classes of Graphs." Algorithms 11, no. 10: 161.
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