Wiener index of hexagonal chains under some transformations

The Wiener index is a topological index of a molecule, defined as the sum of distances between all pairs of vertices in the chemical graph. Hexagonal chains consist of hexagonal rings connected with each other by edges. This class of chains contains molecular graphs of unbranched catacondensed benzenoid hydrocarbons. A segment of length ℓ of a chain is its maximal subchain with ℓ linear annelated hexagons. We consider chains in which all segments have equal lengths. Such chains can be uniquely represented by binary vectors. The Wiener index of hexagonal chains under some operations on the corresponding binary vectors are investigated. The obtained results may be useful in studying of topological indices for sets of hexagonal chains induced by algebraic constructions.