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

Abstract

Abstract In this paper, we establish bounds on the domination number and the metric dimension of the co-normal product graph GH $G_{H}$ 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 $G_{H}$ is 1, 2, and the domination number of G. Moreover, we give formulas for the metric dimension of the co-normal product GH $G_{H}$ of some families of graphs G and H as a function of associated parameters of G and H.

Keywords

• Dominating set
• Resolving set
• Adjacency resolving set
• Co-normal product of graphs