Vertex-transitive Graphs On Fewer Than 48 Vertices This dataset contains all the vertex-transitive graphs on 10-47 vertices. It consists of a collection of tar files, with names like alltrans26.tar meaning that this tar file contains all the vertex-transitive graphs on 26 vertices. Once the tar file is unpacked (using "tar xf alltrans26.tar") this will create a number of smaller gzipped files with names such as alltrans26_k=03.gz meaning that this file contains all the transitive graphs on 26 vertices with degree (valency) 3. Once the gzip file is unpacked using "gunzip alltrans26_k=03.gz" the resulting file contains all the graphs, one per line, in graph6 format (this format was invented by Brendan McKay and is recognised by SageMath). The first five lines of the file alltrans26_k=03 are as follows: Ys???C????_CA?@?`?_GO?c?@_?Q??K??O@CG?aA?GAG@?OCCG?GGC?? Ys??WO@?O??O?J?E?A_H??A?C??O?????_?DC?AQ?AAA??oG?C_O?I?? Ys??WWG@?@?A?W?c??g?S?@??G???G??O??S??I?_?Ac??SS??OW??_? Ys?GGSG@?@?A?W?c??g?S?@??G???G??O??S??I?_?Ac??SS??OW??_? Ys?GOO?????c?Q?c?B?@_?I?A??G??A?@?CCC?OP?CCC?C_O?AOC?C_? These can be directly used as input to SageMath with commands such as g = Graph("Ys???C????_CA?@?`?_GO?c?@_?Q??K??O@CG?aA?GAG@?OCCG?GGC??") No attempt has been made to reduce data storage by removing redundancy. So the tar file for vertex-transitive graphs on n vertices contains files for each feasible valency from 0 to n-1, despite the redundancy inherent in storing both a graph and its complement, and in storing both disconnected and connected graphs.

{"references": ["Derek Holt and Gordon Royle, A census of small transitive groups and vertex-transitive graphs, https://arxiv.org/abs/1811.09015"]}