Volume :2 , Issue :4 ,Page :198-208

Abstract : For a graph G, let V(G) and E(G) denote it s vertex set and edge set respectively. Let V  (G) = {v  : v  V(G)} be a copy of V(G). The Super duplicat e graph with respect to complementation D c *(G) of G is the graph whose vertex set is V(G)  V  (G) and edge set is E(G)  E(D(  G)) where D(  G) is the Duplicate graph of the complement  G of G. In this paper, some basic properties of D c *(G) are studied. Also a criterion for D c *(G) to be Eulerian and a sufficient co ndition for Hamiltonicity are obtained. In addition, the parameters girth, connectivity, cove ring number, independen ce number, chromatic number determined for th is graph. Finally, eccentricity properties of D c *(G) are discussed.