On dynamic colouring of cartesian product of complete graph with some graphs
K. Kaliraj, Hari Naresh Kumar, J. Vernold Vivin · Journal of Taibah University for Science · 2020
A proper vertex colouring is called a 2-dynamic colouring, if for every vertex v with degree at least 2, the neighbours of v receive at least two colours. The smallest integer k such that G has a dynamic colouring with k colours denoted by χ2(G). We denote the cartesian product of G and H by G◻H. In this paper, we find the 2-dynamic chromatic number of cartesian product of complete graph with complete graph Kr◻Ks, complete graph with complete bipartite graph Kn◻K1,s and wheel graph with complete graph Wl◻Kn.