ST-coloring of some products of graphs

Abstract

For a finite set T of non negative integers containing zero, a function c: V(G) → Z+∪{0} is said to be a ST-coloring of the graph G = (V,E), if |c(x) − c(y)| is not in T for any any edge (x, y) and for any two distinct edges (x, y) and (u, v), |c(x)−c(y)|≠|c(u)−c(v)|. spST (G) is the minimum of the difference between the largest and smallest colors assigned over all the vertices and espST (G) is the minimum of the maximum difference between the colors assigned to the vertices of an edge over all the edges of the graph, where the minimum is taken over all ST-coloring c. Here we establish some results related to ST-chromatic number, span and edge span of some graph products namely, Tensor product, Cartesian product and Corona product of graphs.