The Number of Shortest Paths in the (n, k)-Star Graphs

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.

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Euler numbers and diametral paths in Fibonacci cubes, Lucas cubes and alternate Lucas cubes

Eğecioǧlu

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2023

Discrete Math. Algorithm. Appl.

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The Number of Shortest Paths in the (n, k)-Star Graphs

Cited by 1 publication

References 15 publications

Euler numbers and diametral paths in Fibonacci cubes, Lucas cubes and alternate Lucas cubes

Euler numbers and diametral paths in Fibonacci cubes, Lucas cubes and alternate Lucas cubes

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