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In this paper, we investigate the edge-Wiener index, the Szeged index, theedge-Szeged index, and the PI index, which are some of the most studieddistance-based topological indices. As the main result we show that forbenzenoid systems these indices can be computed in sub-linear time with respectto the number of vertices. More precisely, they can be computed in the timedependent on the length of the boundary cycle of a benzenoid system.

The Edge-Wiener Index, the Szeged Indices and the PI Index of Benzenoid Systems in Sub-Linear Time