Independent Middle Domination Number in Graphs

The Middle graph of a graphG, denoted by M(G) ,is a graph whose vertex set is V(G)∪E(G),and two vertices are adjacent if they are adjacent edges of G or one is a vertex and other is a edge incident with it . A set S of vertices of graph M(G) is an independent dominating set of M(G) if S is an independent set and every vertex not in S is adjacent to a vertex inS. The independent middle domination number of G , denoted by iM(G) is the minimum cardinality of an independent dominating set ofM(G) . In this paper many bounds on iM(G) were obtained in terms of the vertices ,edges and other different parameters of G and not in terms of the elements of M(G).Further its relation with other different domination parameters are also obtained.