20.500.12556/DKUM-95616 Relations between polynomials based on perfect matchings and independent sets of CERS In 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. graph theory resonance graphs polynomials teorija grafov resonančni grafi polinomi true false true Angleški jezik Slovenski jezik Znanstveno delo 2025-10-01 10:49:43 2025-10-01 10:49:43 2025-10-02 03:19:52 0000-00-00 00:00:00 2026 0 0 str. 487-508 št. 2 Letn. 95 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 2025-05-20 0000-00-00 0000-00-00 519.17 251239683 10.46793/match.95-2.12125 3009-4399 RAZ_Tratnik_Niko_2026.pdf RAZ_Tratnik_Niko_2026.pdf 1 63C7BEDC9EABDB99174C1EBA8F58179C 811bc4333a6dacdbc0e3b6ca84c2cbecff3aaea1bdb2b0e53a24ca0a3b0f3adf 163d09cf-9ea4-11f0-823e-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=199447 https://match.pmf.kg.ac.rs/issues/m95n2/m95n2_12125.html 1 93a749c7-9ea3-11f0-823e-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=199446 Fakulteta za naravoslovje in matematiko Fakulteta za kemijo in kemijsko tehnologijo 0 0 0