| Title: | Weighted Padovan graphs |
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| Authors: | ID Iršič Chenoweth, Vesna (Author)
ID Klavžar, Sandi (Author)
ID Rus, Gregor (Author)
ID Tan, Elif (Author) |
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| Files: |  PDF - Presentation file, download (720,09 KB)
MD5: A4640CC8404E1A49793F08AE42884DCF
 URL - Source URL, visit https://www.sciencedirect.com/science/article/pii/S0012365X25000652
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | Weighted Padovan graphs $\Phi^{n}_{k}$, $n \geq 1$, $\lfloor \frac{n}{2} \rfloor \leq k \leq \lfloor \frac{2n-2}{3} \rfloor$, are introduced as the graphs whose vertices are all Padovan words of length $n$ with $k$ $1$s, two vertices being adjacent if one can be obtained from the other by replacing exactly one $01$ with a $10$. By definition, $\sum_k |V(\Phi^{n}_{k})|=P_{n+2}$, where $P_n$ is the $n$th Padovan number. Two families of graphs isomorphic to weighted Padovan graphs are presented. The order, the size, the degree, the diameter, the cube polynomial, and the automorphism group of weighted Padovan graphs are determined. It is also proved that they are median graphs. |
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| Keywords: | Padovan sequence, weighted Padovan graph, integer partition, median graphs |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.07.2025 |
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| Year of publishing: | 2025 |
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| Number of pages: | 12 str. |
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| Numbering: | Vol. 348, iss. 7, article no. 114457 |
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| PID: | 20.500.12556/DiRROS-23893  |
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| UDC: | 519.17 |
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| ISSN on article: | 0012-365X |
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| DOI: | 10.1016/j.disc.2025.114457 |
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| COBISS.SI-ID: | 227687939 |
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| Publication date in DiRROS: | 20.10.2025 |
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| Views: | 159 |
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| Downloads: | 66 |
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