On the Fibonacci numbers of the molecular graphs of some bent phenylenes

Abstract

The Fibonacci number f (G) of a graph G = (V;E) is defined as the number of all subsets U of V such that no two vertices in U are adjacent. Phenylenes represent a class of condensed polycyclic conjugated compounds which have the molecular graph possessing both six-membered and four-membered circuits. In this paper we are concerned with special types of bent phenylenes expanding our previous results on the linear phenylenes. The explicit formulas for the Fibonacci numbers of the bent phenylenes are found as functions of the number n of hexagons in both mentioned branches of phenylene.