Volume :7 , Issue :2 ,Page : 48-59

Abstract : The dominating graph D m G bcd (G) of a graph G is obtained from G with vertex set V  = V(G)  S, where V = V(G) and S is the set of all
-sets of G. Two elements in V  are said to satisfy property ‘a’ if u, v  V  and are adjacent in G. Two elements in V  are said to satisfy property ‘b’ if u = D 1 , v = D 2  S such that D 1 and D 2 have a common vertex. Two elements in V  are said to satisfy property ‘c’ if u  V(G), v = D  S such that u  D. Two elements in V  are said to satisfy property ‘d’ if u, v  V(G) and there exists D  S such that u, v  D. A graph having vertex set V  and any two elements in V  are adjacent if they satisfy any one of the property b, c, d is denoted by D m G bcd (G). In this paper, we have studied some basic properties of D m G bcd (G). Also, we have characterized graphs G for which D m G bcd (G) has some specific properties and we have established some extremal properties of D m G bcd (G)