斐波那契立方体、卢卡斯立方体和交替卢卡斯立方体中的欧拉数和直径路径

IF 0.6 Q4 MATHEMATICS, APPLIED

Discrete Mathematics Algorithms and Applications Pub Date : 2022-10-25 DOI:10.1142/s1793830923500271

O. Egecioglu, Elif Saygı, Zülfükar Saygı

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引用次数: 1

摘要

图的直径是图中顶点对之间的最大距离。一对顶点的距离等于其直径的顶点称为对径顶点。在完全相反的顶点之间的最短路径的集合被称为直径路径。在这项工作中，我们列举了Fibonacci立方体，Lucas立方体和Alternate Lucas立方体的直径路径的数量。我们给出了客观的证明，证明这些数与交替排列有关，并由欧拉数枚举。

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Euler Numbers and Diametral Paths in Fibonacci Cubes, Lucas Cubes and Alternate Lucas Cubes

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 are called diametrically opposite vertices. The collection of shortest paths between diametrically opposite vertices are 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.

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来源期刊

Discrete Mathematics Algorithms and Applications MATHEMATICS, APPLIED-

CiteScore

1.50

自引率

41.70%

发文量

129