Total Colorings of Some Classes of FourRegular Circulant Graphs

R. Navaneeth; J. Geetha; K. Somasundaram; Hung-Lin Fu

Total Colorings of Some Classes of FourRegular Circulant Graphs

Combinatorics 2021-11-01 v1

Authors: R. Navaneeth , J. Geetha , K. Somasundaram , Hung-Lin Fu

Abstract

The total chromatic number, $\chi''(G)$ is the minimum number of colors which need to be assigned to obtain a total coloring of the graph $G$ . The Total Coloring Conjecture (TCC) made independently by Behzad and Vizing that for any graph, $\chi''(G) \leq \Delta(G)+2$ , where $\Delta(G)$ represents the maximum degree of $G$ . In this paper we obtained the total chromatic number for some classes of four regular circulant graphs.

Keywords

total coloring total chromatic number circulant graph regular graph coloring conjecture

Cite

@article{arxiv.2110.15592,
  title  = {Total Colorings of Some Classes of FourRegular Circulant Graphs},
  author = {R. Navaneeth and J. Geetha and K. Somasundaram and Hung-Lin Fu},
  journal= {arXiv preprint arXiv:2110.15592},
  year   = {2021}
}

Total Colorings of Some Classes of FourRegular Circulant Graphs

Abstract

Keywords

Cite

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