Panconnectivity, fault-tolerant hamiltonicity and hamiltonian-connectivity in alternating group graphs

  • Authors:

  • Jou-Ming Chang;Jinn-Shyong Yang;Yue-Li Wang;Yuwen Cheng

  • Affiliations:

  • Department of Information Management, National Taipei College of Business, No. 321, Section 1, Tsi Nan Road, Taipei, Taiwan, Republic of China;Department of Information Management, National Taipei College of Business, No. 321, Section 1, Tsi Nan Road, Taipei, Taiwan and DepT. of Info. Mgmt., Natl. Taiwan Univ. of Sci. and Technol., Taipe ...;Department of Information Management, National Taiwan University of Science and Technology, Taipei, Taiwan, Republic of China;Department of Mathematics, National Taitung University, Taitung, Taiwan, Republic of China

  • Venue:
  • Networks
  • Year:
  • 2004

Quantified Score

Hi-index 0.01

Visualization

Abstract

Jwo et al. [Networks 23 (1993) 315–326] introduced the alternating group graph as an interconnection network topology for computing systems. They showed that the proposed structure has many advantages over n-cubes and star graphs. For example, all alternating group graphs are hamiltonian-connected (i.e., every pair of vertices in the graph are connected by a hamiltonian path) and pancyclic (i.e., the graph can embed cycles with arbitrary length with dilation 1). In this article, we give a stronger result: all alternating group graphs are panconnected, that is, every two vertices x and y in the graph are connected by a path of length k for each k satisfying d(x, y) ≤ k ≤ |V| - 1, where d(x, y) denotes the distance between x and y, and |V| is the number of vertices in the graph. Moreover, we show that the r-dimensional alternating group graph AGr, r ≥ 4, is (r - 3)-vertex fault-tolerant Hamiltonian-connected and (r - 2)-vertex fault-tolerant hamiltonian. The latter result can be viewed as complementary to the recent work of Lo and Chen [IEEE Trans. Parallel and Distributed Systems 12 (2001) 209–222], which studies the fault-tolerant hamiltonicity in faulty arrangement graphs. © 2004 Wiley Periodicals, Inc. NETWORKS, Vol. 44(4), 302–310 2004