Cayley graphs

This page lists all the Cayley graphs on up to 31 vertices, but divided according to the group to which they belong. This may be important for some applications, otherwise this data is largely a repetition of data that can be found in the lists of transitive graphs.

The first group of each order is the cyclic group, then the remaining groups are ordered according to the lists in the book Group Tables by Thomas & Wood (this book omits the cyclic groups). They give some descriptive names, which I have stuck to (with the exception of using D(2n) for the dihedral group of order 2n, rather than D(n)). The cryptic names for the groups of order 16 come from Hall and Senior.

All graphs are in the graph6 format. If you are going to download large files, you may want to consider these points.

Each file contains only those graphs whose degree is less than n/2, connected or otherwise. If you want all the graphs, it will be necessary to find the complements. The numbers given in the table are the number of graphs in each file - usually this is half the number of Cayley graphs for that group, but if n = 4k+1 then the ones of degree 2k would get counted twice if we just doubled the number.