Computing the Matching Polynomials and Independence Polynomials of Phenylene Chains

Abstract

Phenylene, a significant structural motif in organic chemistry, exhibits remarkable electron delocalization and stability. In this paper, we first present reduction formulas for computing the matching polynomial and the independence polynomial of any phenylene chain using the transfer matrix technique. We then derive computational formulas for the Hosoya index and the Merrifield–Simmons index of phenylene chains. Additionally, we obtain the expected values of the Hosoya index and the Merrifield–Simmons index for a random phenylene chain.