| Title: | Relations between polynomials based on perfect matchings and independent sets of CERS |
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| Authors: | ID Tratnik, Niko (Author)
ID Žigert Pleteršek, Petra (Author) |
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| Files: |  RAZ_Tratnik_Niko_2026.pdf (473,85 KB)
MD5: 63C7BEDC9EABDB99174C1EBA8F58179C
 https://match.pmf.kg.ac.rs/issues/m95n2/m95n2_12125.html
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| Language: | English |
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| Work type: | Scientific work |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | FNM - Faculty of Natural Sciences and Mathematics
FKKT - Faculty of Chemistry and Chemical Engineering
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| Abstract: | 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. |
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| Keywords: | graph theory, resonance graphs, polynomials |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Submitted for review: | 20.05.2025 |
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| Year of publishing: | 2026 |
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| Number of pages: | str. 487-508 |
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| Numbering: | Letn. 95, št. 2 |
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| PID: | 20.500.12556/DKUM-95616  |
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| UDC: | 519.17 |
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| ISSN on article: | 3009-4399 |
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| COBISS.SI-ID: | 251239683 |
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| DOI: | 10.46793/match.95-2.12125 |
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| Publication date in DKUM: | 01.10.2025 |
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| Views: | 261 |
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| Downloads: | 13 |
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| Metadata: |    |
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| Categories: | Misc.
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