Bounds on the domination number and the metric dimension of co-normal product of graphs

Abstract

In this paper, we establish bounds on the domination number and the metric dimension of the co-normal product graph GH of two simple graphs G and H in terms of parameters associated with G and H. We also give conditions on the graphs G and H for which the domination number of GH is 1, 2, and the domination number of G. Moreover, we give formulas for the metric dimension of the co-normal product GH of some families of graphs G and H as a function of associated parameters of G and H.