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V.R. Kulli, B. Chaluvaraju and H.S. Boregowda

Abstract

Let G = (V, E) be a connected graph with vertex set V (G) and edge set E(G). The product connectivity Banhatti index of a graph G is defined as, PB(G)=ue1dG(u)dG(e) where ue means that the vertex u and edge e are incident in G. In this paper, we determine P B(G) of some standard classes of graphs. We also provide some relationship between P B(G) in terms of order, size, minimum / maximum degrees and minimal non-pendant vertex degree. In addition, we obtain some bounds on P B(G) in terms of Randić, Zagreb and other degree based topological indices of G.