• THE OPEN EDGE NEIGHBORHOOD GRAPH AND THE COMMON EDGE NEIGHBORHOOD GRAPH OF A GRAPH

Abstract

Let G = (V, E) be a graph. For any edge eÎE, the open edge neighborhood set N(e) of e is the set of edges adjacent to e. The open edge neighborhood graph N_oe(G) of a graph G is defined to be the intersection graph on the family of all open edge neighborhood sets of edges in G. The common edge neighborhood graph N_ce (G) of G is the graph having the vertex set E and with the two vertices in N_ce(G) are adjacent if there exists an open edge neighborhood set in G containing them. In this paper, we initiate a study of these new graphs.