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Kekulé structure of angularly connected even ring systems
ID Brezovnik, Simon (Avtor)

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Izvleček
An even ring system G is a simple 2-connected plane graph with all interior vertices of degree 3, all exterior vertices of either degree 2 or 3, and all finite faces of an even length. G is angularly connected if all of the peripheral segments of G have odd lengths. In this paper, we show that every angularly connected even ring system G, which does not contain any triple of altogether-adjacent peripheral faces, has a perfect matching. This was achieved by finding an appropriate edge coloring of G, derived from the proof of the existence of a proper face 3-coloring of the graph. Additionally, an infinite family of graphs that are face 3-colorable has been identified. When interpreted in the context of the inner dual of G, this leads to the introduction of 3-colorable graphs containing cycles of lengths 4 and 6, which is a supplementation of some already known results. Finally, we have investigated the concept of the Clar structure and Clar set within the aforementioned family of graphs. We found that a Clar set of an angularly connected even ring system cannot in general be obtained by minimizing the cardinality of the set A. This result is in contrast to the previously known case for the subfamily of benzenoid systems, which admit a face 3-coloring. Our results open up avenues for further research into the properties of Clar and Fries sets of angularly connected even ring systems.

Jezik:Angleški jezik
Ključne besede:Kekulé structure, Clar structure, perfect matching, benzenoid system, even ring system, face coloring, edge coloring, Clar set
Vrsta gradiva:Članek v reviji
Tipologija:1.01 - Izvirni znanstveni članek
Organizacija:FS - Fakulteta za strojništvo
Status publikacije:Objavljeno
Različica publikacije:Objavljena publikacija
Leto izida:2024
Št. strani:14 str.
Številčenje:Vol. 13, iss. 12, [art. no.] 827
PID:20.500.12556/RUL-165200 Povezava se odpre v novem oknu
UDK:519.17
ISSN pri članku:2075-1680
DOI:10.3390/axioms13120827 Povezava se odpre v novem oknu
COBISS.SI-ID:216596995 Povezava se odpre v novem oknu
Datum objave v RUL:27.11.2024
Število ogledov:89
Število prenosov:16
Metapodatki:XML DC-XML DC-RDF
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Gradivo je del revije

Naslov:Axioms
Skrajšan naslov:Axioms
Založnik:MDPI
ISSN:2075-1680
COBISS.SI-ID:519951897 Povezava se odpre v novem oknu

Licence

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

Projekti

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

Financer:ARRS - Agencija za raziskovalno dejavnost Republike Slovenije
Številka projekta:J1-4031
Naslov:Računalniška knjižnica za zavozlane strukture in aplikacije

Financer:ARRS - Agencija za raziskovalno dejavnost Republike Slovenije
Številka projekta:J2-2512
Naslov:Stohastični modeli za logistiko proizvodnih procesov

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