Strong Domination in Middle Graph

Abstract

For any two adjacent vertices u and v we say that v is strongly dominates u, if deg. A dominating set D is a strong dominating set of , if every vertex in is strongly dominated by at least one vertex in D. A strong domination number of a middle graph  is the minimum cardinality of a strong dominating set of and is denoted by . In this paper, we determine best possible upper and lower bounds for  in terms of elements of G and related to other domination parameters of G. Keywords: Graph, Middle Graph, Strong Dominating set Strong Domination N