Enumerating $k$-matchings in cyclic chains using the transfer matrix technique

Klavžar, Sandi (author), Grad, Simon (author)

A cyclic chain is a plane graph whose all inner faces are cycles and its inner dual is isomorphic to a path. In this paper, the transfer matrix technique using the $k$-matching vector is developed to compute the number of $k$-matchings in an arbitrary cyclic chain. This extends similar methods developed earlier in two papers for benzenoid chains and for octagonal chains. The method is illustrated on the flourene molecule.

• Language: English
• Keywords: matchings, Hosoya index, cyclic chains, transfer matrix, k-matching vector, Toeplitz matrix
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Publication date: 01.01.2025
• Year: 2025
• Number of pages: Str. 645-658
• Numbering: Vol. 94, no. 3
• PID: 20.500.12556/RUL-168988
• UDC: 519.17
• ISSN on article: 3009-4399
• DOI: 10.46793/match.94-3.26824
• COBISS.SI-ID: 234927875
• Publication date in RUL: 06.05.2025

Record is a part of a journal

• Title: Match
• Shortened title: Match
• Publisher: Faculty of Science, University of Kragujevac
• ISSN: 3009-4399
• COBISS.SI-ID: 186294787

Licences

• 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.

Secondary language

• Language: Slovenian
• Keywords: prirejanje, Hosoyev indeks, ciklične verige, prehodna matrika, vektor k-prirejanj, Toeplitzova matrika