A special class of conjugated hydrocarbons known as phenylenes, which is composed of a special arrangement of six- and four-membered rings. In particular, any two six-membered rings (hexagons) are not adjacent, and every four-membered ring(square) is adjacent to a pair of nonadjacent hexagons. If each hexagon of phenylene is adjacent only to two squares, then the obtained chain is called the phenylene chain. The main object of this paper is to determine the expected values of the sum-connectivity, harmonic, and symmetric division indices of this class of conjugated hydrocarbons. The comparisons between the expected values of these indices with respect to the random phenylene chains have been determined explicitly. The graphical illustrations have been given in terms of the differences between the expected values of these indices.
The polyphenyl chains with $n$ hexagons are the special graphs of unbranched polycyclic aromatic hydrocarbons. The objective of this study is to find the expected values of the multiplicative version of the atomic-bond connectivity index and geometric-arithmetic index of this class of special hydrocarbons. The average values of these two indices with respect to the set of all polyphenyl chains have been determined. Finally, the comparisons between the expected values of the aforementioned indices in the random polyphenyl and spiro chains, have been outlined.