Vertex-transitive Graphs On Fewer Than 48 Vertices

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.

顶点数少于48的顶点传递图数据集

本数据集收录了所有顶点数介于10至47之间的顶点传递图（vertex-transitive graph）。

本数据集由一系列tar压缩包组成，文件名格式如`alltrans26.tar`，该压缩包内含顶点数为26的全部顶点传递图。

将该tar包解压（执行命令`tar xf alltrans26.tar`）后，会生成若干小型gzip压缩文件，例如`alltrans26_k=03.gz`，该文件包含顶点数为26、价数（valency）为3的全部顶点传递图。

使用`gunzip alltrans26_k=03.gz`解压该gzip文件后，得到的文件将以graph6格式存储所有图数据，每行对应一幅图。该格式由Brendan McKay发明，可被SageMath识别。

文件`alltrans26_k=03`的前五行示例如下：
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_?

这些数据可直接作为输入供SageMath使用，示例命令如下：`g = Graph("Ys???C????_CA?@?`?_GO?c?@_?Q??K??O@CG?aA?GAG@?OCCG?GGC??")`

本数据集未通过移除冗余数据来压缩存储空间。因此，针对顶点数为n的顶点传递图的tar包，会为0至n-1范围内所有可行的价数生成对应的文件，即便存储图及其补图、同时存储连通与非连通图会带来固有冗余。