Lists of Undirected Graphs

Undirected Graphs:

These correspond to pure quadratic polynomials over the integers mod 2. The number of such graphs (up to isomorphism) with n vertices is well-known -- it is sequence A000088 in the On-Line Encyclopedia of Integer Sequences.

Here I have lists of the graphs in the following format. A graph on n vertices is represented by the upper half of its adjacency matrix, specifically as n-1 strings separated by spaces, where the i'th string has length i and the j'th letter of the string denotes whether vertex i+1 has an edge to vertex j. The different graphs are listed in lexicographic order applied to these strings.

Much more extensive listings, in another format, are available from Brendan McKay of Australian National University. (Hat tip again to Don Knuth.)

Two-Colored Graphs:

I am also interested in pure quadratic polynomials over other rings such as the integers mod 3. These are represented by graphs where the edges, when present, can have one of two colors, "1" or "2". The number of these with n vertices is also in the On-Line Encyclopedia as sequence A004102 -- these "signed graphs" were first enumerated by Harary in the 1950's. (Thanks to Don Knuth for this reference.) Here are lists, in a format similar to the above, of:

Last modified 31 May 2007