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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: | Egecioglu, Omer Saygi, Elif Saygi, Zulfukar |
Keywords: | Shortest Path Diametral Path Fibonacci Cube Lucas Cube Alternate Lucas Cube Euler Number |
Publisher: | World Scientific Publ Co Pte Ltd | 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. | URI: | https://doi.org/10.1142/S1793830923500271 | ISSN: | 1793-8309 1793-8317 |
Appears in Collections: | Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection |
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