Edge Jump Distance Graphs

Abstract

The concept of edge jump between graphs and distance between graphs was introduced by Gary Chartrand et al. in [5]. A graph H is obtained from a graph G by an edge jump if G contains four distinct vertices u, v, w, and x such that uv belongs to  E(G), wx does not belong to E(G) and H isomorphic to G ¢â‚¬uv + wx. The concept of edge rotations and distance between graphs was first introduced by Chartrand et.al [4]. A graph H is said to be obtained from a graph G by a single edge rotation if G contains three distinct vertices u, v, and w such that uv belongs to \ ‚ E(G) and uw does not belong to ‚ E(G). If a graph H is obtained from a graph G by a sequence of edge jumps, then G is said to be j-transformed into H. In this paper we consider edge jumps on generalized Petersen graphs G_p(n,1) and cycles. We have also developed an algorithm that gives self-centered graphs and almost self-centered graphs through edge jumps followed by some general results on edge jum