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The Atom-Bond Connectivity and Geometric-Arithmetic Indices in Random Polyphenyl Chains

Abstract The atom-bond connectivity (ABC) index and geometric-arithmetic (GA) index are two well-studied topological indices and found to be useful tools in QSPR and QSAR investigations. We have compared the excepted values of ABC and GA indices in random spiro chains. In this paper, we further establish simple explicit formulae for the expected values of ABC and GA indices in random polyphenyl chains which are graphs of a class of unbranched polycyclic aromatic hydrocarbons and present the average values of ABC and GA indices with respect to the set of all polyphenyl chains with n hexagons. Based on these formulae, we make comparisons between the expected values of ABC and GA indices in random polyphenyl chains.