Connected Domination in Middle Graph

Abstract

       The middle graph of a graph G, denoted by is a graph whose vertex set is   and two vertices are adjacent if they are adjacent edges of G or one is a vertex and other is an edge incident with it. A dominating set D of  is called a connected dominating set of  if the induced subgraph  is connected. The minimum cardinality of D is called the connected domination number of  and is denoted by .