Dominations in semigraphs

Abstract

The semigraph generalization is more closely related to the axiom that the two edges in a semigraph have atmost one vertex in common, where as the hypergraph generalization is based on the consideration of an edge as a subset of two elements of the set of vertices of graphs. The concept of domination is an important parameter in graph theory. They provide a lot of space to the theoretical development of graphs and their applications. The dominations in semigraphs have no exception. In this paper, we study various dominations of semigraphs arising out of the corresponding adjacencies exist in semigraphs.