Abstract

Mathematical properties of many topological indices are investigated. Knor et al. gave an upper bound for the Balaban index of r-regular graphs on n vertices and a better upper bound for fullerene graphs. They also suggested exploring similar bounds for other topological indices. In this paper, we consider the Sum-Balaban index and the (revised) Szeged index, and give upper and lower bounds for these three indices of r-regular graphs, and also the cubic graphs and fullerene graphs, respectively.

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