A Structured Table of Graphs with Symmetries and Other Special Properties

TL;DR

This paper presents a comprehensive table of optimized regular graphs with various desirable properties, discovered through large-scale enumeration, which could be valuable for designing efficient network topologies.

Contribution

It introduces a structured catalog of optimal graphs with symmetries and minimal diameters, many of which are newly identified, advancing the understanding of graph properties for practical applications.

Findings

Discovered numerous new optimal graphs with high symmetry.

Provided a structured enumeration of graphs with minimal diameters.

Highlighted potential applications in network topology design.

Abstract

We organize a table of regular graphs with minimal diameters and minimal mean path lengths, large bisection widths and high degrees of symmetries, obtained by enumerations on supercomputers. These optimal graphs, many of which are newly discovered, may find wide applications, for example, in design of network topologies.