Geodesic-bipancyclicity of balanced hypercubes

ABSTRACT

The 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.

KEYWORDS:

• Interconnection networks
• bipancyclic
• geodesic cycles
• geodesic-bipancyclic
• balanced hypercubes

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 05C38
• 68R10

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Huazhong Lü  http://orcid.org/0000-0003-1033-2386

Additional information

Funding

This research was partially supported by the National Natural Science Foundation of China [grants numbers 11261019, 11361024] and Natural Science Foundation of Jiangxi Province [grants number 20161BAB201030].