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The atom-bond connectivity ( ABC ) index and geometric–arithmetic ( GA ) index are two well-studied topological indices, which are useful tools in QSPR and QSAR investigations. In this paper, we first obtain explicit formulae for the expected values of  ABC  and  GA  indices in random spiro chains, which are graphs of a class of unbranched polycyclic aromatic hydrocarbons. Based on these formulae, we then present the average values of  ABC  and  GA  indices with respect to the set of all spiro chains with  n  hexagons and make a comparison between the expected values of  ABC  and  GA  indices in random spiro chains.

Comparing the excepted values of atom-bond connectivity and geometric–arithmetic indices in random spiro chains