A note on the independence polynomial of 3-regular 2-connected planar graphs

Abstract

Our work examines the independence polynomial of 3-regular 2-connected planar (3R2CP) graphs by introducing a novel, formulaic approach centered on an iterative construction method. The core of our contribution is decomposing the constructed graphs into specific subgraphs, for which we first determine the individual independence polynomials. This decomposition strategy provides a straightforward pathway to systematically calculate the independence polynomial for the entire 3R2CP graph class formed by the given construction technique, representing a new methodological advancement in chemical graph theory. By offering this clear process, our research not only presents a new family of graphs with computable indices but also provides a practical analytical tool to enable more efficient analysis of the structure-property relationships these graphs represent.