Applying Latin Square on Parallel Routing of Alternating Group Graphs

Abstract

A major topic of studying communication networks is to nd an appropriate route for mes- sage transmission. In particular, the design of parallel routing can be used to transmit mul- tiple packets eÆciently from a source node to a destination node simultaneously. In this pa- per, we consider the problem of constructing parallel routes in an alternating group graph, which has recently been developed as a new model of the interconnection topology for par- allel and distributed computing systems. An n- alternating group graph contains (n!)=2 nodes and is a regular graph with degree 2(n 2) for each node. The aim of our work is to provide an algorithm for constructing 2(n2) edge-disjoint paths for any pair of nodes in an n-alternating group graph for a special case. Furthermore, we show that the lengths of all paths are shortest.