Abstract

A set  is dominating set of edge semi-middle graph, if every vertex not in D is adjacent to a vertex in D. The domination number of the edge semi-middle graph denoted by  is the minimum cardinality of dominating set of edge semi-middle graph . We study the graph theoretic properties of  and its exact values for some standard graphs. The relation between  with other dominating parameters are also investigated.

Keywords

Covering number; Dominating Set; Edge Semi-Middle graph

Introduction