Edge H-domination in graph

Abstract

This paper is about edge H-domination of the graph. The edge H-dominating set is defined and the characterization of a minimal edge H-dominating set of the graph with minimum degree 2 is given. The upper bound on the edge H-domination number of the graph is discussed. The changes in the edge H-domination number are observed under vertex(edge) removal operation on graph. The concepts called weak isolated edge and edge H-private neighborhood of the graph are defined.