Minimal Cayley graphs on 2 to 511 vertices (excluding 384)

A Cayley graph Cay(G,S) is minimal if S defines an inclusion-minimal generating set of G. A complete list of all minimal Cayley graphs on up to 511 vertices has been determined (33645009 graphs in total). Group theoretical computations were performed using GAP, while reduction modulo graph isomorphism was done using Nauty. We plan to publish details of the enumerative methods and computational techniques used in the near future. This work extends the collection of Kolja Knauer found at the House of graphs, and is also available at graphsym.net. The resulting graphs are available in sparse6 format. The file below contains all Cayley graphs of order 2 to 511, except those of order 384 (9317394 graphs). Extracting the downloaded file will place one file for each order <n> between 2 and 511, named mincay_<n>.s6, into your current directory. The minimal Cayley graphs of order 384 are stored separately.若集合S构成群G的包含极小生成集，则凯莱图（Cayley graph）Cay(G,S)为极小凯莱图。目前已完成顶点数不超过511的全部极小凯莱图的完整列表编制，总计33645009张。本研究采用GAP完成群论相关计算，使用Nauty完成图同构约简操作。我们计划在近期公开本次研究中使用的枚举方法与计算技术细节。本数据集拓展了Kolja Knauer在图之家（House of graphs）发布的数据集集合，同时可通过graphsym.net获取。本次生成的极小凯莱图均以sparse6格式存储。下述压缩文件包含阶数2至511的全部极小凯莱图（阶数384的图除外，总计9317394张）。解压下载的压缩文件后，当前目录下将生成每个阶数<n>（2≤n≤511）对应的文件，文件命名格式为mincay_<n>.s6。阶数384的极小凯莱图将单独存储。