Coupon coloring of lexicographic product of graphs
T. Reji, Pavithra Rajamani · The Art of Discrete and Applied Mathematics · 2022
A k-coupon coloring of a graph G without isolated vertices is an assignment of colors from [k] = {1, 2, …, k} to the vertices of G such that the neighborhood of every vertex of G contains vertices of all colors from [k]. The maximum k for which a k-coupon coloring exists is called the coupon coloring number of G. In this paper, we have studied the coupon coloring number of Lexicographic product of graphs G and H if G has a Hamiltonian path. We have found a sharp bound for the coupon coloring number of Lexicographic product of connected graphs.