Horadam-Lucas cubes

Tan, Elif (author), Podrug, Luka (author), Iršič Chenoweth, Vesna (author)

In this paper, we introduce a novel class of graphs referred to as the Horadam–Lucas cubes. This class extends the concept of Lucas cubes and retains numerous desirable properties associated with them. Horadam–Lucas cubes can also be viewed as a companion graph family of the Horadam cubes, in a similar way the Lucas cubes relate to Fibonacci cubes or the Lucas-run graphs relate to Fibonacci-run graphs. As special cases, they also give rise to new graph families, such as Pell–Lucas cubes and Jacobsthal–Lucas cubes. We derive the several metric and enumerative properties of these cubes, including their diameter, periphery, radius, fundamental decomposition, number of edges, cube polynomials, and generating function of the cube polynomials.

• Language: English
• Keywords: hypercubes, Lucas cubes, Horadam-Lucas sequence, Horadam-Lucas cubes, partial cubes
• 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: 01.12.2024
• Year: 2024
• Number of pages: 16 str.
• Numbering: Vol. 13, iss. 12, [article no.] 837
• PID: 20.500.12556/RUL-166038
• UDC: 519.17
• ISSN on article: 2075-1680
• DOI: 10.3390/axioms13120837
• COBISS.SI-ID: 219677443
• Publication date in RUL: 18.12.2024

Record is a part of a journal

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

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: hiperkocke, Lucasove kocke, Horadam-Lucasovo zaporedje, Horadam-Lucasove kocke, delne kocke