The Structure of K-Lucas Cubes

Abstract

Fibonacci cubes and Lucas cubes have been studied as alternatives for the classical hy-percube topology for interconnection networks. These families of graphs have interesting graph theoretic and enumerative properties. Among the many generalization of Fibonacci cubes are k-Fibonacci cubes, which have the same number of vertices as Fibonacci cubes, but the edge sets determined by a parameter k. In this work, we consider k-Lucas cubes, which are obtained as subgraphs of k-Fibonacci cubes in the same way that Lucas cubes are obtained from Fibonacci cubes. We obtain a useful decomposition property of k-Lucas cubes which allows for the calculation of basic graph theoretic properties of this class: the number of edges, the average degree of a vertex, the number of hypercubes they contain, the diameter and the radius. © 2021, Hacettepe University. All rights reserved.