Bounds on the Balaban Index

The Balaban index of a connected (molecular) graph G is defined as J = J(G) = m μ+1 Σ uv∈E(G) (D u D v ) -1/2 where m is the number of edges, μ is the cyclomatic number, D u is the sum of distances between vertex u and all other vertices of G, and the summation goes over all edges from the edge set E(G). The Balaban index is one of the widely used topological indices for QSAR and QSPR studies. In this paper, tight lower and upper bounds are reported for the Balaban index.