Table of large graphs with given degree and diameter

TL;DR

This work updates the large-graph, degree–diameter table for undirected graphs by compiling post-2013 results obtained via diverse construction techniques, including vertex augmentation, symmetric-graph methods, semidirect products of cyclic groups, and Cayley graphs from groups of order $648$. It highlights concrete new entries (e.g., $(13,3)=856$, $(3,8)=360$, and a $648$-order Cayley graph) and provides computational tools and adjacency data in Com26. The paper emphasizes that these constructions push the known frontier toward the Moore bound for small diameters and degrees, while offering downloadable resources for researchers to study and verify the graphs. Overall, it expands practical knowledge of extremal order graphs for the degree–diameter problem and supplies concrete examples and data for network design and related applications.

Abstract

We update the table of large undirected graphs with given degree and diameter with results obtained since the publication of the survey by M. Miller and J. Širáň in the {\em Electronic Journal of Combinatorics} (Dynamic Survey DS14, 2nd. edition. May 2013).