F-average eccentric graphs

Abstract

The -average eccentric graph of a graph has the vertex set as in and any two vertices and are adjacent in if either they are at a distance while is connected or they are in different components while is disconnected. A graph is called a -average eccentric graph if for some graph . The main aim of this paper is to find a necessary and sufficient condition for a graph to be a -average eccentric graph.

AMS (2000) subject classifications: 05C12