Horadam–Lucas Cubes
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 simi...
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MDPI AG
2024-11-01
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| Online Access: | https://www.mdpi.com/2075-1680/13/12/837 |
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| author | Elif Tan Luka Podrug Vesna Iršič Chenoweth |
| author_facet | Elif Tan Luka Podrug Vesna Iršič Chenoweth |
| author_sort | Elif Tan |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-964d741223ec43418305ed7306d935f3 |
| institution | OA Journals |
| issn | 2075-1680 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-964d741223ec43418305ed7306d935f32025-08-20T02:00:51ZengMDPI AGAxioms2075-16802024-11-01131283710.3390/axioms13120837Horadam–Lucas CubesElif Tan0Luka Podrug1Vesna Iršič Chenoweth2Department of Mathematics, Faculty of Science, Ankara University, 06100 Ankara, TürkiyeFaculty of Civil Engineering, University of Zagreb, 10000 Zagreb, CroatiaFaculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana, SloveniaIn 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.https://www.mdpi.com/2075-1680/13/12/837hypercubeLucas cubeHoradam–Lucas sequenceHoradam–Lucas cubepartial cube |
| spellingShingle | Elif Tan Luka Podrug Vesna Iršič Chenoweth Horadam–Lucas Cubes Axioms hypercube Lucas cube Horadam–Lucas sequence Horadam–Lucas cube partial cube |
| title | Horadam–Lucas Cubes |
| title_full | Horadam–Lucas Cubes |
| title_fullStr | Horadam–Lucas Cubes |
| title_full_unstemmed | Horadam–Lucas Cubes |
| title_short | Horadam–Lucas Cubes |
| title_sort | horadam lucas cubes |
| topic | hypercube Lucas cube Horadam–Lucas sequence Horadam–Lucas cube partial cube |
| url | https://www.mdpi.com/2075-1680/13/12/837 |
| work_keys_str_mv | AT eliftan horadamlucascubes AT lukapodrug horadamlucascubes AT vesnairsicchenoweth horadamlucascubes |