The edge-Hosoya polynomial of benzenoid chains

TL;DR

This paper introduces the edge-Hosoya polynomial for benzenoid chains, deriving recurrence relations and solutions specifically for linear chains called polyacenes, linking graph theory to molecular structure analysis.

Contribution

It defines and analyzes the edge-Hosoya polynomial for benzenoid chains, providing recurrence relations and explicit solutions for linear cases, advancing molecular graph descriptors.

Findings

Derived recurrence relations for edge-Hosoya polynomial of benzenoid chains

Solved recurrence relations for linear benzenoid chains (polyacenes)

Connected edge-Hosoya polynomial to molecular structure descriptors

Abstract

The Hosoya polynomial is a well known vertex-distance based polynomial, closely correlated to the Wiener index and the hyper-Wiener index, which are widely used molecular-structure descriptors. In the present paper we consider the edge version of the Hosoya polynomial. For a connected graph $G$ let $d_e(G,k)$ be the number of (unordered) edge pairs at distance $k$. Then the edge-Hosoya polynomial of $G$ is $H_e(G,x) = \sum_{k \geq 0} d(G,k)x^k$. We investigate the edge-Hosoya polynomial of important chemical graphs known as benzenoid chains and derive the recurrence relations for them. These recurrences are then solved for linear benzenoid chains, which are also called polyacenes.