Here is some information about the 34 graphs on 5 vertices, keyed to the graph reference numbers employed by Peter Steinbach in his "Field Guide to Simple Graphs". The vertices in each graph are labelled from 1 to 5. Each line of the file corresponds to a graph, and contains the following information: (1) Steinbach's reference number for the graph. (2) The degree sequence of the graph as a string of 5 digits, with the degree of vertex 5 first, then the degree of vertex 4, and so on down to the degree of vertex 1. (3) The edge set of the graph, with each edge listed as the pair of digits corresponding to its two vertices. Note that if N(G) is the reference number of a graph G, and N(G^c) is the reference number of the complement of G, then N(G) + N(G^c) = 35, except that Graphs 16 and 18 are complements, and Graphs 17 and 19 are self-complementary. Graph 1: | Degree Sequence is 00000 | (No edges) Graph 2: | Degree Sequence is 00011 | Edge 12 Graph 3: | Degree Sequence is 00112 | Edges 12 13 Graph 4: | Degree Sequence is 01111 | Edges 12 34 Graph 5: | Degree Sequence is 00222 | Edges 12 13 23 Graph 6: | Degree Sequence is 01113 | Edges 12 13 14 Graph 7: | Degree Sequence is 01122 | Edges 12 13 24 Graph 8: | Degree Sequence is 11112 | Edges 12 13 45 Graph 9: | Degree Sequence is 01223 | Edges 12 13 14 23 Graph 10: | Degree Sequence is 02222 | Edges 12 13 24 34 Graph 11: | Degree Sequence is 11114 | Edges 12 13 14 15 Graph 12: | Degree Sequence is 11123 | Edges 12 13 14 25 Graph 13: | Degree Sequence is 11222 | Edges 12 13 23 45 Graph 14: | Degree Sequence is 11222 | Edges 12 13 24 35 Graph 15: | Degree Sequence is 02233 | Edges 12 13 14 23 24 Graph 16: | Degree Sequence is 12223 | Edges 12 13 14 23 45 Graph 17: | Degree Sequence is 22222 | Edges 12 13 24 35 45 Graph 18: | Degree Sequence is 12223 | Edges 12 13 14 25 35 Graph 19: | Degree Sequence is 11233 | Edges 12 13 14 23 25 Graph 20: | Degree Sequence is 11224 | Edges 12 13 14 15 23 Graph 21: | Degree Sequence is 22233 | Edges 12 13 14 23 25 45 Graph 22: | Degree Sequence is 22233 | Edges 12 13 14 25 35 45 Graph 23: | Degree Sequence is 12333 | Edges 12 13 14 23 24 35 Graph 24: | Degree Sequence is 03333 | Edges 12 13 14 23 24 34 Graph 25: | Degree Sequence is 22224 | Edges 12 13 14 15 23 45 Graph 26: | Degree Sequence is 12234 | Edges 12 13 14 15 23 24 Graph 27: | Degree Sequence is 23333 | Edges 12 13 14 23 24 35 45 Graph 28: | Degree Sequence is 22334 | Edges 12 13 14 15 23 24 35 Graph 29: | Degree Sequence is 13334 | Edges 12 13 14 15 23 24 34 Graph 30: | Degree Sequence is 22244 | Edges 12 13 14 15 23 24 25 Graph 31: | Degree Sequence is 33334 | Edges 12 13 14 15 23 24 35 45 Graph 32: | Degree Sequence is 23344 | Edges 12 13 14 15 23 24 25 34 Graph 33: | Degree Sequence is 33444 | Edges 12 13 14 15 23 24 25 34 35 Graph 34: | Degree Sequence is 44444 | Edges 12 13 14 15 23 24 25 34 35 45