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Title: Euler numbers and diametral paths in Fibonacci cubes, Lucas cubes and alternate Lucas cubes
Authors: Egecioğlu, Ömer
Saygı, Elif
Saygi, Zulfukar
Keywords: Shortest path
diametral path
Fibonacci cube
Lucas cube
alternate Lucas cube
Euler number
Issue Date: 2023
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.
Description: Article; Early Access
ISSN: 1793-8309
Appears in Collections:Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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