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https://hdl.handle.net/20.500.11851/10472| Title: | Euler Numbers and Diametral Paths in Fibonacci Cubes, Lucas Cubes and Alternate Lucas Cubes |
| Authors: | Eǧeci˙oǧlu,Ö. Saygi,E. Saygi,Z. |
| Keywords: | alternate Lucas cube diametral path Euler number Fibonacci cube Lucas cube Shortest path |
| Publisher: | World Scientific |
| Abstract: | The diameter of a graph is the maximum distance between pairs of vertices in the graph. A pair of vertices whose distance is equal to its diameter is called diametrically opposite vertices. The collection of shortest paths between diametrically opposite vertices is referred as diametral paths. In this work, we enumerate the number of diametral paths for Fibonacci cubes, Lucas cubes and alternate Lucas cubes. We present bijective proofs that show that these numbers are related to alternating permutations and are enumerated by Euler numbers. © 2024 World Scientific Publishing Company. |
| URI: | https://doi.org/10.1142/S1793830923500271 https://hdl.handle.net/20.500.11851/10472 |
| ISSN: | 1793-8309 |
| Appears in Collections: | Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection |
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