Total Colouring of New Classes of Subcubic graphs

Authors

Sethuraman G, Anna University, ChennaiFollow
Velankanni Anthonymuthu, Sathyabama Institute of Science and TechnologyFollow

Publication Date

July 2022

Abstract

The total chromatic number of a graph G, denoted χ”(G), is the least number of colours needed to colour the vertices and the edges of G such that no incident or adjacent elements (vertices or edges) receive the same colour. The popular Total Colouring Conjecture (TCC) posed by Behzad states that, for every simple graph G, χ”(G) ≤ Δ(G)+2. In this paper, we prove that the total chromatic number for a family of subcubic graphs called cube connected paths and also for a class of subcubic graphs having the property that the vertices are covered by independent triangles are exactly Δ(G)+1. More precisely, these two families of subcubic graphs are shown to be Type 1 graph.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

Recommended Citation

G, Sethuraman and Anthonymuthu, Velankanni (2022) "Total Colouring of New Classes of Subcubic graphs," Theory and Applications of Graphs: Vol. 9: Iss. 2, Article 7.
DOI: 10.20429/tag.2022.090207
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol9/iss2/7