On hinge domination in graphs

Abstract

A set Dh of vertices in a graph G = (V,E) is a hinge dset if every vertex u in V −Dh is adjacent to some vertex v in Dh and a vertex w in V −Dh such that (v,w) is not an edge in E. The hinge domination number γh(G) is the minimum size of a hinged dset. In this paper we determine hinge domination number γh(G) for standard graphs and some shadow distance graphs.