Graph distance measures based on Balaban indices

Abstract

Dehmer et al. [Interrelations of graph distance measures based on topological indices, PLoS One 9 (2014) e94985] explored the graph measures based on some topological indices and demonstrated some useful properties of them. In this work, we survey the graph measures based on the Balaban index of a graph, and prove some extremal properties on them for several classes of graphs. Moreover, through numerical calculation and comparison, we find the graph measures based on Balaban index of a graph behave better than that based on Randić index in some special cases.