Generalized Pell graphs

Iršič, Vesna (author), Klavžar, Sandi (author), Tan, Elif (author)

In this paper, generalized Pell graphs $\Pi_{n,k}$, $k\ge 2$, are introduced. The special case of $k=2$ are the Pell graphs $\Pi_{n}$ defined earlier by Munarini. Several metric, enumerative, and structural properties of these graphs are established. The generating function of the number of edges of $\Pi_{n,k}$ and the generating function of its cube polynomial are determined. The center of $\Pi_{n,k}$ is explicitly described; if $k$ is even, then it induces the Fibonacci cube $\Gamma_{n}$. It is also shown that $\Pi_{n,k}$ is a median graph, and that $\Pi_{n,k}$ embeds into a Fibonacci cube.

• Language: English
• Keywords: Fibonacci cubes, Pell graphs, generating functions, center of graph, median graphs, $k$-Fibonacci sequence
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2023
• Number of pages: Str. 1955-1973
• Numbering: Vol. 47, no. 7, art. 9
• PID: 20.500.12556/RUL-155600
• UDC: 519.17
• ISSN on article: 1300-0098
• DOI: 10.55730/1300-0098.3475
• COBISS.SI-ID: 179971075
• Publication date in RUL: 08.04.2024

Record is a part of a journal

• Title: Turkish journal of mathematics
• Publisher: Scientific and Technical Research Council of Turkey
• ISSN: 1300-0098
• COBISS.SI-ID: 512342809

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: Fibonaccijeve kocke, Pellovi grafi, rodovne funkcije, center grafa, medianski grafi, $k$-Fibonaccijevo zaporedje