论文标题
斐波那契立方体，卢卡斯方块和替代卢卡斯立方体中的欧拉数和直径路径
Euler numbers and diametral paths in Fibonacci cubes, Lucas cubes and Alternate Lucas cubes
论文作者
论文摘要
图的直径是图中顶点对之间的最大距离。一对距离等于其直径的顶点称为直径相反的顶点。直径相反的顶点之间最短路径的收集称为直径路径。在这项工作中，我们列举了斐波那契立方体，卢卡斯立方体和交替的卢卡斯立方体的直径路径数量。我们提出了展示这些数字与交替排列相关的徒证明，并被Euler数字列举。
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.
