Vertex-bipancyclicity of the generalized honeycomb tori

Yuan-Kang Shih, Yi-Chien Wu, Shin Shin Kao*, Jiann-Mean Tan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Assume that m, n and s are integers with m >= 2, n >= 4, 0 <= s < n and s is of the same parity of m. The generalized honeycomb tori GHT(m, n, s) have been recognized as an attractive architecture to existing torus interconnection networks in parallel and distributed applications. A bipartite graph G is bipancyclic if it contains a cycle of every even length from 4 to vertical bar V(G)vertical bar inclusive. G is vertex-bipancyclic if for any vertex nu is an element of V(G), there exists a cycle of every even length from 4 to vertical bar V(G)vertical bar that passes nu. A bipartite graph G is called k-vertex-bipancyclic if every vertex lies on a cycle of every even length from k to vertical bar V(G)vertical bar. In this article, we prove that GHT(m, n, s) is 6-bipancyclic, and is bipancyclic for some special cases. Since GHT(m. n. s) is vertex-transitive, the result implies that any vertex of GHT(m. n. s) lies on a cycle of length l, where l >= 6 and is even. Besides, GHT(m, n, s) is vertex-bipancyclic in some special cases. The result is optimal in the sense that the absence of cycles of certain lengths on some GHT(m, n. s)'s is inevitable due to their hexagonal structure. (C) 2008 Elsevier Ltd. All rights reserved.
Original languageEnglish
Pages (from-to)2848-2860
JournalComputers and Mathematics with Applications
Volume56
Issue number11
DOIs
StatePublished - Dec 2008

Keywords

  • Honeycomb torus; Pancyclic; Bipancyclic; Vertex-bipancyclic; k-vertex-bipancyclic

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