A new class of interconnection networks based on alternating group

Abstract

This paper introduces a new class of interconnection scheme based on the Cayley graph of the alternating group. It is shown that this class of graphs are edge symmetric and 2-transitive. We then describe an algorithm for (a) packet routing based on the shortest path analysis, (b) finding a Hamiltonian cycle, (c) ranking and unranking along the chosen Hamiltonian cycle, (d) unit expansion and dilation three embedding of a class of two-dimensional grids, (e) unit dilation embedding of a variety of cycles, and (f) algorithm for broadcasting messages. The paper concludes with a short analysis of contention resulting from a typical communication scheme. Although this class of graphs does not possess many of the symmetry properties of the binary hypercube, with respect to the one source broadcasting, these graphs perform better than does a hypercube, and with respect to the contention problem, these graphs perform better than do the star graphs and are close to the hypercube. 0 1993 by John Wiley & Sons, Inc.

Linearly many faults in 2‐tree‐generated networks

“…The star graph, proposed by [1], has many advantages over the n-cube such as lower degree and smaller diameter. Since its introduction, a number of additional classes have been introduced; the most popular ones are the alternating group graphs [17], their companion graphs, the split-stars [7], and further generalizations such as the (n, k)-star graphs [13] and the arrangement graphs [14]. These interconnection networks have gathered considerable attention with many papers written on them in a wide range of areas such as topological properties, broadcasting issues, fault-tolerant routing, strong connectivity, and vulnerability issues as well as fault-tolerant Hamiltonian properties.…”

The 2-Extra Diagnosability of Alternating Group Graphs under the PMC Model and MM* Model

“…As a favorable topology structure of interconnection networks, alternating group graphs have been shown to have many desirable properties such as strong hierarchy, high connectivity, small diameter and average distance, etc. For details, see [19] for a comparison of the hypercube, the star graph and the alternating group graph. …”

Construction of vertex-disjoint paths in alternating group networks

“…The alternating group network AN n , which has a construction similar to the star graph, was proposed by Youhu [27] to improve upon the alternating group graph AG n , originally advocated by Jwo, Lakshmivarahan, and Dhall [16,17]. Chen, Xiao, and Parhami [4] presented an optimal routing algorithm for the class of alternating group networks.…”