Status connectivity indices and co-indices of graphs and its computation to some distance-balanced graphs

Abstract

The status of a vertex , denoted by , is the sum of the distances between and all other vertices in a graph . The first and second status connectivity indices of a graph are defined as and respectively, where denotes the edge set of . In this paper we have defined the first and second status co-indices of a graph as and respectively. Relations between status connectivity indices and status co-indices are established. Also these indices are computed for intersection graph, hypercube, Kneser graph and achiral polyhex nanotorus.

Keywords

• distance in graph
• status indices
• distance-balanced graphs