Volume :5 , Issue :3 ,Page : 66-75

Abstract : For any graph G, define the Equi-eccentric po int set graph G ee , on the same set of vertices, by joining two vertices in G ee if and only if they correspond to two vertices of G with equal eccentricities. Also, define the Glue graph G g on the same set of vertices by joining two vertices in G g if and only if they correspond to two adjacent vertices of G or two adjacent vertices of G ee and define the complement Glue graph G cg on the same set of vertices by joining two vertices in G cg if and only if they correspond to two adjacent vertices of  G or two adjacent vertices of G ee . In this paper, the concept of Equi-eccentric point set graph, Glue graph and co mplement Glue graph of a graph are introduced and some general and structural properties of G ee , G g and G cg are presented.