Order Adjustment Approach Using Cayley Graphs for the Order/Degree Problem

抄録

The order/degree problem consists of finding the smallest diameter graph for a given order and degree. Such a graph is beneficial for designing low-latency networks with high performance for massively parallel computers. The average shortest path length (ASPL) of a graph has an influence on latency. In this paper, we propose a novel order adjustment approach. In the proposed approach, we search for Cayley graphs of the given degree that are close to the given order. We then adjust the order of the best Cayley graph to meet the given order. For some order and degree pairs, we explain how to derive the smallest known graphs from the Graph Golf 2016 and 2017 competitions.