Physical Sciences and Mathematics Commons^™

Total Colouring Of New Classes Of Subcubic Graphs, Sethuraman G, Velankanni Anthonymuthu

Theory and Applications of Graphs

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 …