Orienting split-stars and alternating group graphs

Abstract

Akers et al. proposed an interconnection topology, the star graph, as an alternative to the popular n‐cube. Cheng et al. proposed the split‐star as an alternative to the star graph and a companion graph to the alternating group graph proposed by Jwo et al. Star graphs, alternating group graphs, and split‐stars are advantageous over n‐cubes in many aspects. Day and Tripathi proposed an assignment of directions to the edges of the star graph and showed that the resulting directed graph is strongly connected and has a simple routing algorithm. In this paper, we give simple routing algorithms for a proposed orientation of alternating group graphs and split‐stars. The resulting directed graphs are not only strongly connected but they have maximal arc‐fault tolerance and a small diameter. © 2000 John Wiley & Sons, Inc.

Survey on path and cycle embedding in some networks

“…An n-dimensional alternating group graph, denoted by AG n , proposed by Jwo et al [98] and further investigated by Cheng et al [31][32][33], is an undirected graph with vertices labelled with even permutations on a set of the symbols 1, 2, . .…”

An optimal result on fault-tolerant cycle-embedding in alternating group graphs

“…Alternating group graphs were first proposed by Jwo et al [8] and further investigated by Cheng and Lipman [9][10][11]. This family of graphs has been shown to have many nice properties including vertex-transitivity, edgetransitivity, strongly hierarchy, maximally connectivity (i.e., the connectivity equals to the regularity in a graph), and has small diameter and average distance.…”

An efficient distributed algorithm for canonical labeling on directed split-stars

“…The directed split-stars are not only strongly connected, but, in fact, they have maximal arc-fault tolerance for connectivity and a small diameter [3][4][5]. Recently, Wang et al developed efficient distributed algorithms to obtain the unique minimum distance-k dominating sets, for k = 1, 2, and minimal feedback vertex sets on n-dimensional directed split-stars [13,14].…”