On Hinge Domination of Tent and Umbrella Graphs

Abstract

A set  of vertices in a graph G with vertex set V and edge set E is considered a hinge-dominating set if, for every vertex  in  there exists a vertex  in  and a vertex in   such that the edge  is not present in E.The hinge domination number represents the minimum size of the hinge dominating set of graph G. In this paper, we determine the exact values of  for a selection of basic graphs, an umbrella graph, and a Mongolian tent graph