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Naslov: The multivariable Zhang-Zhang polynomial of phenylenes ID Tratnik, Niko (Avtor) Tratnik-2023-The_Multivariable_Zhang-Zhang_Pol.pdf (719,26 KB)MD5: 5934C26509350FB4EF432B001A85A7ED  https://doi.org/10.3390/axioms12111053 Angleški jezik Znanstveno delo 1.01 - Izvirni znanstveni članek FNM - Fakulteta za naravoslovje in matematiko The Zhang-Zhang polynomial of a benzenoid system is a well-known counting polynomial that was introduced in 1996. It was designed to enumerate Clar covers, which are spanning subgraphs with only hexagons and edges as connected components. In 2018, the generalized Zhang-Zhang polynomial of two variables was defined such that it also takes into account 10-cycles of a benzenoid system. The aim of this paper is to introduce and study a new variation of the Zhang-Zhang polynomial for phenylenes, which are important molecular graphs composed of 6-membered and 4-membered rings. In our case, Clar covers can contain 4-cycles, 6-cycles, 8-cycles, and edges. Since this new polynomial has three variables, we call it the multivariable Zhang-Zhang (MZZ) polynomial. In the main part of the paper, some recursive formulas for calculating the MZZ polynomial from subgraphs of a given phenylene are developed and an algorithm for phenylene chains is deduced. Interestingly, computing the MZZ polynomial of a phenylene chain requires some techniques that are different to those used to calculate the (generalized) Zhang-Zhang polynomial of benzenoid chains. Finally, we prove a result that enables us to find the MZZ polynomial of a phenylene with branched hexagons. Zhang-Zhang polynomial, phenylene, Clar cover, Kekulé structure Objavljeno Objavljena publikacija 06.10.2023 14.11.2023 15.11.2023 MDPI 2023 Str. 1-18 Letn. 12, Št. 11, št. članka 1053 20.500.12556/DKUM-87024 519.17 172554499 10.3390/axioms12111053 2075-1680 09.02.2024 65 2 Ostalo Kopiraj citat

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Naslov: Axioms Axioms MDPI 2075-1680 519951897

## Gradivo je financirano iz projekta

Financer: ARRS - Agencija za raziskovalno dejavnost Republike Slovenije P1-0297 Teorija grafov

Financer: ARRS - Agencija za raziskovalno dejavnost Republike Slovenije N1-0285 Metrični problemi v grafih in hipergrafih

## Licence

Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna http://creativecommons.org/licenses/by/4.0/deed.sl To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja. 15.11.2023

## Sekundarni jezik

Jezik: Slovenski jezik Zhang-Zhangov polinom, fenilen, Clarovo število, Kekuléjeva struktura

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