Chromatic numbers of certain hypercube variants

Abstract

The total (vertex/edge) chromatic number of a graph G, χ ″ ( G ) ( χ ( G ) / χ ′ ( G ) ) is defined to be the minimum number of colours needed to colour the vertices and edges, together termed as elements (vertices/edges) of a graph in such a way that no two adjacent/incident elements (vertices/edges) are given the same colour. In this article, we determine the vertex, edge and total chromatic number of some hypercube variants such as folded hypercube, enhanced hypercube, augmented hypercube and exchanged hypercube.