The expected values of some indices in random phenylene chains

Abstract

A special class of conjugated hydrocarbons is 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, symmetric division, variable inverse sum degree and general Randic indices for 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.