Bipanconnectivity and edge-fault-tolerant bipancyclicity of hypercubes

  • Authors:

  • Tseng-Kuei Li;Chang-Hsiung Tsai;Jimmy J. M. Tan;Lih-Hsing Hsu

  • Affiliations:

  • Department of Computer Science and Information Engineering, Ching Yun Institute of Technology JungLi 320, Taiwan, R.O.C.;Department of Computer Science and Information Engineering, Ching Yun Institute of Technology JungLi 320, Taiwan, R.O.C.;Department of Computer and Information Science, National Chiao Tung University, Hsinchu 30050, Taiwan, R.O.C.;Department of Computer and Information Science, National Chiao Tung University, Hsinchu 30050, Taiwan, R.O.C.

  • Venue:
  • Information Processing Letters
  • Year:
  • 2003

Quantified Score

Hi-index 0.90

Visualization

Abstract

A bipartite graph is bipancyclic if it contains a cycle of every even length from 4 to |V(G)| inclusive. It has been shown that Qn is bipancyclic if and only if n ≥ 2. In this paper, we improve this result by showing that every edge of Qn - E' lies on a cycle of every even length from 4 to |V(G)| inclusive where E' is a subset of E(Qn) with |E'| ≤ n - 2. The result is proved to be optimal. To get this result, we also prove that there exists a path of length l joining any two different vertices x and y of Qn when h(x, y) ≤ l ≤ |V(G)| - 1 and l - h(x, y) is even where h(x, y) is the Hamming distance between x and y.