Geodesic-bipancyclicity of balanced hypercubes

Abstract

ABSTRACTThe hypercube is one of the most important interconnection networks because of its simple structure and desirable properties. As a variant of hypercube, the balanced hypercube was proposed as a novel network topology for parallel systems. A bipartite graph G is called geodesic-bipancyclic if, for each pair of vertices , it contains a geodesic cycle with u and v of each even length l, where max. In this paper, we prove that the balanced hypercube is geodesic-bipancyclic for all , which improves some known results.