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Title:Kekulé structure of angularly connected even ring systems
Authors:ID Brezovnik, Simon (Author)
Files:.pdf PDF - Presentation file, download (315,29 KB)
MD5: 9884C77D6855F3DDD63FE35C14356FDA
 
URL URL - Source URL, visit https://www.mdpi.com/2075-1680/13/12/827
 
Language:English
Typology:1.01 - Original Scientific Article
Organization:Logo IMFM - Institute of Mathematics, Physics, and Mechanics
Abstract: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.
Keywords:Kekulé structure, Clar structure, perfect matching, benzenoid system, even ring system, face coloring, edge coloring, Clar set
Publication status:Published
Publication version:Version of Record
Publication date:01.01.2024
Year of publishing:2024
Number of pages:str. 1-14
Numbering:Vol. 13, iss. 12, [art. no.] 827
PID:20.500.12556/DiRROS-21066 New window
UDC:519.17
ISSN on article:2075-1680
DOI:10.3390/axioms13120827 New window
COBISS.SI-ID:216596995 New window
Note:
Publication date in DiRROS:18.12.2024
Views:200
Downloads:96
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BREZOVNIK, Simon, 2024, Kekulé structure of angularly connected even ring systems. Axioms [online]. 2024. Vol. 13, no. 12,  827, p. 1–14. [Accessed 21 April 2025]. DOI 10.3390/axioms13120827. Retrieved from: https://dirros.openscience.si/IzpisGradiva.php?lang=eng&id=21066
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Record is a part of a journal

Title:Axioms
Shortened title:Axioms
Publisher:MDPI
ISSN:2075-1680
COBISS.SI-ID:519951897 New window

Document is financed by a project

Funder:ARRS - Slovenian Research Agency
Project number:P1-0297
Name:Teorija grafov
Funder:ARRS - Slovenian Research Agency
Project number:J1-4031
Name:Računalniška knjižnica za zavozlane strukture in aplikacije
Funder:ARRS - Slovenian Research Agency
Project number:J2-2512
Name:Stohastični modeli za logistiko proizvodnih procesov

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License:CC BY 4.0, Creative Commons Attribution 4.0 International
Link:http://creativecommons.org/licenses/by/4.0/
Description:This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

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