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The polyphenyl chains with  n  hexagons are the special graphs of unbranched polycyclic aromatic hydrocarbons. The main objective of this study is to find the expected values of the harmonic and second Zagreb indices of this class of hydrocarbons. The average values of the harmonic and second Zagreb indices with respect to the set of all random polyphenyl and spiro chains have been determined. Finally, the comparisons between the expected values of these indices with respect to the random polyphenyl and spiro chains, have been outlined.

The Harmonic and Second Zagreb Indices in Random Polyphenyl and Spiro Chains