Here is some information about the 156 graphs on 6 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 6. 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 6 digits, with the degree of vertex 6 first, then the degree of vertex 5, 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) = 157. Graph 1: | Degree Sequence is 000000 | (No edges) Graph 2: | Degree Sequence is 000011 | Edge 12 Graph 3: | Degree Sequence is 000112 | Edges 12 13 Graph 4: | Degree Sequence is 001111 | Edges 12 34 Graph 5: | Degree Sequence is 000222 | Edges 12 13 23 Graph 6: | Degree Sequence is 001113 | Edges 12 13 14 Graph 7: | Degree Sequence is 001122 | Edges 12 13 24 Graph 8: | Degree Sequence is 011112 | Edges 12 13 45 Graph 9: | Degree Sequence is 111111 | Edges 12 34 56 Graph 10: | Degree Sequence is 001223 | Edges 12 13 14 23 Graph 11: | Degree Sequence is 002222 | Edges 12 13 24 34 Graph 12: | Degree Sequence is 011114 | Edges 12 13 14 15 Graph 13: | Degree Sequence is 011123 | Edges 12 13 14 25 Graph 14: | Degree Sequence is 011222 | Edges 12 13 24 35 Graph 15: | Degree Sequence is 011222 | Edges 12 13 23 45 Graph 16: | Degree Sequence is 111113 | Edges 12 13 14 56 Graph 17: | Degree Sequence is 111122 | Edges 12 13 24 56 Graph 18: | Degree Sequence is 111122 | Edges 12 13 45 46 Graph 19: | Degree Sequence is 002233 | Edges 12 13 14 23 24 Graph 20: | Degree Sequence is 011224 | Edges 12 13 14 15 23 Graph 21: | Degree Sequence is 011233 | Edges 12 13 14 23 25 Graph 22: | Degree Sequence is 012223 | Edges 12 13 14 23 45 Graph 23: | Degree Sequence is 012223 | Edges 12 13 14 25 35 Graph 24: | Degree Sequence is 022222 | Edges 12 13 24 35 45 Graph 25: | Degree Sequence is 111115 | Edges 12 13 14 15 16 Graph 26: | Degree Sequence is 111124 | Edges 12 13 14 15 26 Graph 27: | Degree Sequence is 111133 | Edges 12 13 14 25 26 Graph 28: | Degree Sequence is 111223 | Edges 12 13 14 23 56 Graph 29: | Degree Sequence is 111223 | Edges 12 13 14 25 56 Graph 30: | Degree Sequence is 111223 | Edges 12 13 14 25 36 Graph 31: | Degree Sequence is 112222 | Edges 12 13 23 45 46 Graph 32: | Degree Sequence is 112222 | Edges 12 13 24 34 56 Graph 33: | Degree Sequence is 112222 | Edges 12 13 24 35 46 Graph 34: | Degree Sequence is 003333 | Edges 12 13 14 23 24 34 Graph 35: | Degree Sequence is 012234 | Edges 12 13 14 15 23 24 Graph 36: | Degree Sequence is 012333 | Edges 12 13 14 23 24 35 Graph 37: | Degree Sequence is 022224 | Edges 12 13 14 15 23 45 Graph 38: | Degree Sequence is 022233 | Edges 12 13 14 23 25 45 Graph 39: | Degree Sequence is 022233 | Edges 12 13 14 25 35 45 Graph 40: | Degree Sequence is 111225 | Edges 12 13 14 15 16 23 Graph 41: | Degree Sequence is 111234 | Edges 12 13 14 15 23 26 Graph 42: | Degree Sequence is 111333 | Edges 12 13 14 23 25 36 Graph 43: | Degree Sequence is 112224 | Edges 12 13 14 15 23 46 Graph 44: | Degree Sequence is 112224 | Edges 12 13 14 15 26 36 Graph 45: | Degree Sequence is 112233 | Edges 12 13 14 23 24 56 Graph 46: | Degree Sequence is 112233 | Edges 12 13 14 23 25 46 Graph 47: | Degree Sequence is 112233 | Edges 12 13 14 23 45 46 Graph 48: | Degree Sequence is 112233 | Edges 12 13 14 25 26 35 Graph 49: | Degree Sequence is 112233 | Edges 12 13 14 25 35 56 Graph 50: | Degree Sequence is 122223 | Edges 12 13 14 23 45 56 Graph 51: | Degree Sequence is 122223 | Edges 12 13 14 25 35 46 Graph 52: | Degree Sequence is 122223 | Edges 12 13 14 25 36 56 Graph 53: | Degree Sequence is 222222 | Edges 12 13 23 45 46 56 Graph 54: | Degree Sequence is 222222 | Edges 12 13 24 35 46 56 Graph 55: | Degree Sequence is 013334 | Edges 12 13 14 15 23 24 34 Graph 56: | Degree Sequence is 022244 | Edges 12 13 14 15 23 24 25 Graph 57: | Degree Sequence is 022334 | Edges 12 13 14 15 23 24 35 Graph 58: | Degree Sequence is 023333 | Edges 12 13 14 23 24 35 45 Graph 59: | Degree Sequence is 112235 | Edges 12 13 14 15 16 23 24 Graph 60: | Degree Sequence is 112244 | Edges 12 13 14 15 23 24 26 Graph 61: | Degree Sequence is 112334 | Edges 12 13 14 15 23 24 36 Graph 62: | Degree Sequence is 112334 | Edges 12 13 14 15 23 26 36 Graph 63: | Degree Sequence is 113333 | Edges 12 13 14 23 24 34 56 Graph 64: | Degree Sequence is 113333 | Edges 12 13 14 23 24 35 46 Graph 65: | Degree Sequence is 122225 | Edges 12 13 14 15 16 23 45 Graph 66: | Degree Sequence is 122234 | Edges 12 13 14 15 23 26 45 Graph 67: | Degree Sequence is 122234 | Edges 12 13 14 15 23 24 56 Graph 68: | Degree Sequence is 122234 | Edges 12 13 14 15 23 26 46 Graph 69: | Degree Sequence is 122234 | Edges 12 13 14 15 26 36 46 Graph 70: | Degree Sequence is 122333 | Edges 12 13 14 23 24 35 56 Graph 71: | Degree Sequence is 122333 | Edges 12 13 14 23 25 36 45 Graph 72: | Degree Sequence is 122333 | Edges 12 13 14 23 25 45 46 Graph 73: | Degree Sequence is 122333 | Edges 12 13 14 25 26 35 36 Graph 74: | Degree Sequence is 222224 | Edges 12 13 14 15 23 46 56 Graph 75: | Degree Sequence is 222233 | Edges 12 13 14 23 45 46 56 Graph 76: | Degree Sequence is 222233 | Edges 12 13 14 25 26 35 46 Graph 77: | Degree Sequence is 222233 | Edges 12 13 14 23 25 46 56 Graph 78: | Degree Sequence is 222233 | Edges 12 13 14 25 35 46 56 Graph 79: | Degree Sequence is 223333 | Edges 12 13 14 23 24 35 46 56 Graph 80: | Degree Sequence is 223333 | Edges 12 13 14 23 25 36 45 46 Graph 81: | Degree Sequence is 223333 | Edges 12 13 14 23 25 45 46 56 Graph 82: | Degree Sequence is 223333 | Edges 12 13 14 25 26 35 36 45 Graph 83: | Degree Sequence is 133333 | Edges 12 13 14 23 24 35 45 56 Graph 84: | Degree Sequence is 222334 | Edges 12 13 14 15 23 26 36 45 Graph 85: | Degree Sequence is 222334 | Edges 12 13 14 15 23 24 36 56 Graph 86: | Degree Sequence is 222334 | Edges 12 13 14 15 23 26 45 46 Graph 87: | Degree Sequence is 222334 | Edges 12 13 14 15 23 26 46 56 Graph 88: | Degree Sequence is 123334 | Edges 12 13 14 15 23 24 34 56 Graph 89: | Degree Sequence is 123334 | Edges 12 13 14 15 23 24 35 46 Graph 90: | Degree Sequence is 123334 | Edges 12 13 14 15 23 26 36 46 Graph 91: | Degree Sequence is 123334 | Edges 12 13 14 15 23 24 36 46 Graph 92: | Degree Sequence is 033334 | Edges 12 13 14 15 23 24 35 45 Graph 93: | Degree Sequence is 222244 | Edges 12 13 14 15 23 24 26 56 Graph 94: | Degree Sequence is 222244 | Edges 12 13 14 15 26 36 46 56 Graph 95: | Degree Sequence is 122344 | Edges 12 13 14 15 23 24 25 36 Graph 96: | Degree Sequence is 122344 | Edges 12 13 14 15 23 24 26 35 Graph 97: | Degree Sequence is 113344 | Edges 12 13 14 15 23 24 26 34 Graph 98: | Degree Sequence is 023344 | Edges 12 13 14 15 23 24 25 34 Graph 99: | Degree Sequence is 222235 | Edges 12 13 14 15 16 23 24 56 Graph 100: | Degree Sequence is 122335 | Edges 12 13 14 15 16 23 24 35 Graph 101: | Degree Sequence is 113335 | Edges 12 13 14 15 16 23 24 34 Graph 102: | Degree Sequence is 122245 | Edges 12 13 14 15 16 23 24 25 Graph 103: | Degree Sequence is 333333 | Edges 12 13 14 23 25 36 45 46 56 Graph 104: | Degree Sequence is 333333 | Edges 12 13 14 25 26 35 36 45 46 Graph 105: | Degree Sequence is 233334 | Edges 12 13 14 15 23 24 35 46 56 Graph 106: | Degree Sequence is 233334 | Edges 12 13 14 15 23 26 36 45 46 Graph 107: | Degree Sequence is 233334 | Edges 12 13 14 15 23 24 36 46 56 Graph 108: | Degree Sequence is 223344 | Edges 12 13 14 15 23 24 26 34 56 Graph 109: | Degree Sequence is 223344 | Edges 12 13 14 15 23 24 26 35 46 Graph 110: | Degree Sequence is 223344 | Edges 12 13 14 15 23 24 25 36 46 Graph 111: | Degree Sequence is 223344 | Edges 12 13 14 15 23 24 26 35 56 Graph 112: | Degree Sequence is 223344 | Edges 12 13 14 15 23 26 36 46 56 Graph 113: | Degree Sequence is 133344 | Edges 12 13 14 15 23 24 25 34 56 Graph 114: | Degree Sequence is 133344 | Edges 12 13 14 15 23 24 26 35 45 Graph 115: | Degree Sequence is 222444 | Edges 12 13 14 15 23 24 26 35 36 Graph 116: | Degree Sequence is 123444 | Edges 12 13 14 15 23 24 25 34 36 Graph 117: | Degree Sequence is 033444 | Edges 12 13 14 15 23 24 25 34 35 Graph 118: | Degree Sequence is 223335 | Edges 12 13 14 15 16 23 24 34 56 Graph 119: | Degree Sequence is 223335 | Edges 12 13 14 15 16 23 24 35 46 Graph 120: | Degree Sequence is 133335 | Edges 12 13 14 15 16 23 24 35 45 Graph 121: | Degree Sequence is 222345 | Edges 12 13 14 15 16 23 24 25 36 Graph 122: | Degree Sequence is 123345 | Edges 12 13 14 15 16 23 24 25 34 Graph 123: | Degree Sequence is 222255 | Edges 12 13 14 15 16 23 24 25 26 Graph 124: | Degree Sequence is 333344 | Edges 12 13 14 15 23 24 26 35 46 56 Graph 125: | Degree Sequence is 333344 | Edges 12 13 14 15 23 26 36 45 46 56 Graph 126: | Degree Sequence is 333344 | Edges 12 13 14 15 23 24 25 36 46 56 Graph 127: | Degree Sequence is 233444 | Edges 12 13 14 15 23 24 26 35 36 45 Graph 128: | Degree Sequence is 233444 | Edges 12 13 14 15 23 24 25 34 36 56 Graph 129: | Degree Sequence is 233444 | Edges 12 13 14 15 23 24 26 35 45 56 Graph 130: | Degree Sequence is 224444 | Edges 12 13 14 15 23 24 25 34 36 46 Graph 131: | Degree Sequence is 134444 | Edges 12 13 14 15 23 24 25 34 35 46 Graph 132: | Degree Sequence is 044444 | Edges 12 13 14 15 23 24 25 34 35 45 Graph 133: | Degree Sequence is 333335 | Edges 12 13 14 15 16 23 24 35 46 56 Graph 134: | Degree Sequence is 233345 | Edges 12 13 14 15 16 23 24 25 34 56 Graph 135: | Degree Sequence is 233345 | Edges 12 13 14 15 16 23 24 25 36 46 Graph 136: | Degree Sequence is 223445 | Edges 12 13 14 15 16 23 24 25 34 36 Graph 137: | Degree Sequence is 133445 | Edges 12 13 14 15 16 23 24 25 34 35 Graph 138: | Degree Sequence is 223355 | Edges 12 13 14 15 16 23 24 25 26 34 Graph 139: | Degree Sequence is 334444 | Edges 12 13 14 15 23 24 25 34 36 46 56 Graph 140: | Degree Sequence is 334444 | Edges 12 13 14 15 23 24 26 35 36 45 46 Graph 141: | Degree Sequence is 244444 | Edges 12 13 14 15 23 24 25 34 35 46 56 Graph 142: | Degree Sequence is 333445 | Edges 12 13 14 15 16 23 24 25 36 46 56 Graph 143: | Degree Sequence is 333445 | Edges 12 13 14 15 16 23 24 25 34 36 56 Graph 144: | Degree Sequence is 234445 | Edges 12 13 14 15 16 23 24 25 34 35 46 Graph 145: | Degree Sequence is 144445 | Edges 12 13 14 15 16 23 24 25 34 35 45 Graph 146: | Degree Sequence is 333355 | Edges 12 13 14 15 16 23 24 25 26 34 56 Graph 147: | Degree Sequence is 233455 | Edges 12 13 14 15 16 23 24 25 26 34 35 Graph 148: | Degree Sequence is 444444 | Edges 12 13 14 15 23 24 26 35 36 45 46 56 Graph 149: | Degree Sequence is 344445 | Edges 12 13 14 15 16 23 24 25 34 35 46 56 Graph 150: | Degree Sequence is 334455 | Edges 12 13 14 15 16 23 24 25 26 34 35 46 Graph 151: | Degree Sequence is 244455 | Edges 12 13 14 15 16 23 24 25 26 34 35 45 Graph 152: | Degree Sequence is 333555 | Edges 12 13 14 15 16 23 24 25 26 34 35 36 Graph 153: | Degree Sequence is 444455 | Edges 12 13 14 15 16 23 24 25 26 34 35 46 56 Graph 154: | Degree Sequence is 344555 | Edges 12 13 14 15 16 23 24 25 26 34 35 36 45 Graph 155: | Degree Sequence is 445555 | Edges 12 13 14 15 16 23 24 25 26 34 35 36 45 46 Graph 156: | Degree Sequence is 555555 | Edges 12 13 14 15 16 23 24 25 26 34 35 36 45 46 56