On dynamic colouring of cartesian product of complete graph with some graphs

Abstract

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 χ 2 (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 K r K s , complete graph with complete bipartite graph K n K 1,s and wheel graph with complete graph W l K n . ARTICLE HISTORY

On the r-dynamic coloring of some fan graph families

“…Let us also remark that the fan graph F m,n constitutes the join product of a path of order n with a set of m isolated vertices. As such, this paper contributes to solve the dynamic graph coloring problem of graph products, which is receiving particular attention in the recent literature [6,8,15,17]. The study of the r-dynamic chromatic number of the join product of any two graphs is established as further work.…”

On r-hued coloring of product graphs

“…It follows by definition that ∆(𝐺 𝐻) = ∆(𝐺) + ∆(𝐻). Kaliraj et al [4] studied 2-hued chromatic numbers of Cartesian product of complete graph and star graph, for positive integers 𝑠 ≥ 2 and 𝑛,…”