Relations between polynomials based on perfect matchings and independent sets of CERSTratnik, Niko (Avtor) Žigert Pleteršek, Petra (Avtor) graph theoryresonance graphspolynomialsIn this paper, we firstly focus on catacondensed even ring systems (shortly CERS) without any linearly connected adjacent triple of f inite faces. For such a graph G, we describe a bijection between the set of all perfect matchings (Kekulé structures) of G and the set of all independent sets of the inner dual of G, which enables us to prove the equality between three polynomials: the sextet polynomial of G, the independence polynomial of the inner dual of G, and the newly introduced link polynomial of G. These equalities imply that the number of perfect matchings of G equals the number of resonant sets of G and also the number of independent sets of the inner dual of G. Moreover, we show that the number of edges of the resonance graph of G coincides with the derivative of the mentioned polynomials evaluated at x = 1. Finally, we provide the generalization of the results to all peripherally 2-colorable graphs.20262025-10-01 10:49:43Znanstveno delo95616sl