Some Torus-embedded Graphs with Regular Structure Have the Minimum Diameter and the Minimum Average Shortest Path Length
Noriyuki Fujimoto, Kobayashi Hiroyuki · 2018
It is not realistic to connect all of cores in a multicore-processor each other because current multicore-processors have many cores. Therefore there are many studies about network topologies to connect cores. The order/degree problem is one of the tackled problems. It finds graphs with the minimum diameter and the minimum average shortest path length (ASPL) over all graphs for a given number n of vertices and a given degree deg. We present an algorithm to enumerate all of graphs with the minimum diameter and the minimum ASPL over all graphs such that each vertex of torus with n vertices is added edges regularly within degree deg. Also we report optimal graphs for the order/degree problem found by our algorithm.