There are 58 graphs with 0 loops: There are 9 with 0 loops and 0 biedges: [40](0, 0){{6,24},{6,23},{6,7},{7,19},{7,20},{10,18},{10,19},{10,22},{18,21},{18,22},{19,20},{20,24},{21,22},{21,23},{23,24}} [42](0, 0){{6,24},{6,23},{6,7},{7,19},{7,20},{17,19},{17,21},{17,22},{18,19},{18,20},{18,22},{20,24},{21,22},{21,23},{23,24}} [61](0, 0){{6,21},{6,22},{6,7},{7,18},{7,23},{17,18},{17,19},{17,20},{18,23},{19,20},{19,21},{20,24},{21,22},{22,24},{23,24}} [113](0, 0){{8,9},{8,19},{8,21},{9,10},{9,20},{10,18},{10,22},{15,18},{15,19},{15,23},{18,22},{19,21},{20,21},{20,23},{22,23}} [114](0, 0){{8,9},{8,18},{8,20},{9,10},{9,19},{10,21},{10,17},{17,21},{17,22},{18,20},{18,23},{19,20},{19,23},{21,22},{22,23}} [124](0, 0){{4,16},{4,11},{4,22},{11,16},{11,17},{12,18},{12,20},{12,15},{15,20},{15,23},{16,17},{17,18},{18,22},{20,23},{22,23}} [125](0, 0){{4,16},{4,11},{4,23},{11,16},{11,17},{12,19},{12,22},{12,15},{15,19},{15,21},{16,17},{17,23},{19,21},{21,22},{22,23}} [140](0, 0){{3,19},{3,12},{3,13},{11,16},{11,19},{11,15},{12,16},{12,13},{13,14},{14,17},{14,18},{15,17},{15,18},{16,17},{18,19}} [142](0, 0){{3,17},{3,19},{3,12},{11,17},{11,13},{11,14},{12,18},{12,14},{13,16},{13,15},{14,15},{15,18},{16,17},{16,19},{18,19}} There are 15 with 0 loops and 1 biedges: [10](1, 0){{6,10},{6,10},{6,7},{7,11},{7,12},{10,11},{11,12},{12,13},{13,14},{13,23},{14,24},{14,22},{22,24},{22,23},{23,24}} [17](1, 0){{6,10},{6,10},{6,7},{7,11},{7,22},{10,11},{11,21},{12,24},{12,20},{12,22},{20,24},{20,23},{21,22},{21,23},{23,24}} [21](1, 0){{6,9},{6,9},{6,19},{9,19},{10,24},{10,20},{10,22},{18,19},{18,21},{18,22},{20,24},{20,23},{21,22},{21,23},{23,24}} [24](1, 0){{6,10},{6,10},{6,7},{7,11},{7,22},{10,11},{11,20},{19,24},{19,22},{19,23},{20,21},{20,23},{21,24},{21,22},{23,24}} [25](1, 0){{6,10},{6,10},{6,7},{7,22},{7,21},{10,19},{11,24},{11,20},{11,21},{19,22},{19,23},{20,24},{20,23},{21,22},{23,24}} [26](1, 0){{6,24},{6,23},{6,7},{7,22},{7,21},{10,20},{10,13},{10,21},{13,19},{13,23},{19,20},{19,20},{21,22},{22,24},{23,24}} [32](1, 0){{6,9},{6,9},{6,18},{9,18},{17,18},{17,20},{17,22},{19,24},{19,22},{19,23},{20,21},{20,23},{21,24},{21,22},{23,24}} [34](1, 0){{6,24},{6,23},{6,7},{7,22},{7,21},{12,18},{12,20},{12,23},{18,19},{18,19},{19,21},{20,21},{20,22},{22,24},{23,24}} [41](1, 0){{6,10},{6,10},{6,7},{7,20},{7,23},{10,18},{18,24},{18,21},{19,20},{19,21},{19,22},{20,23},{21,22},{22,24},{23,24}} [62](1, 0){{6,10},{6,10},{6,7},{7,24},{7,20},{10,18},{18,22},{18,23},{19,20},{19,21},{19,23},{20,24},{21,24},{21,22},{22,23}} [83](1, 0){{6,16},{6,18},{6,22},{15,24},{15,19},{15,20},{16,22},{16,21},{18,19},{18,19},{20,24},{20,23},{21,22},{21,23},{23,24}} [117](1, 0){{5,19},{5,22},{5,15},{8,18},{8,18},{8,23},{11,16},{11,20},{11,15},{15,19},{16,20},{16,22},{18,23},{19,20},{22,23}} [139](1, 0){{3,19},{3,6},{3,6},{6,13},{12,16},{12,19},{12,15},{13,16},{13,14},{14,17},{14,18},{15,17},{15,18},{16,17},{18,19}} [143](1, 0){{10,17},{10,12},{10,13},{11,13},{11,15},{11,15},{12,16},{12,18},{13,19},{14,17},{14,19},{14,15},{16,17},{16,18},{18,19}} [151](1, 0){{3,19},{3,5},{3,5},{5,6},{6,17},{6,7},{7,18},{7,15},{11,16},{11,17},{11,19},{15,16},{15,18},{16,17},{18,19}} There are 17 with 0 loops and 2 biedges: [3](2, 0){{6,10},{6,10},{6,7},{7,11},{7,12},{10,11},{11,12},{12,13},{13,17},{13,14},{14,24},{14,17},{17,23},{23,24},{23,24}} [6](2, 0){{6,10},{6,10},{6,7},{7,24},{7,11},{10,11},{11,23},{12,24},{12,22},{12,15},{15,21},{15,23},{21,22},{21,22},{23,24}} [11](2, 0){{6,9},{6,9},{6,21},{9,21},{10,24},{10,13},{10,22},{13,19},{13,23},{19,22},{19,22},{20,24},{20,21},{20,23},{23,24}} [14](2, 0){{6,10},{6,10},{6,7},{7,24},{7,23},{10,21},{11,22},{11,14},{11,23},{14,20},{14,21},{20,22},{20,22},{21,24},{23,24}} [16](2, 0){{6,9},{6,9},{6,21},{9,21},{10,11},{10,20},{10,20},{11,12},{11,23},{12,24},{12,22},{20,21},{22,24},{22,23},{23,24}} [22](2, 0){{6,9},{6,9},{6,20},{9,20},{12,18},{12,22},{12,23},{18,21},{18,21},{19,24},{19,20},{19,22},{21,24},{22,23},{23,24}} [23](2, 0){{6,10},{6,10},{6,7},{7,24},{7,23},{10,20},{13,19},{13,20},{13,22},{19,21},{19,21},{20,24},{21,23},{22,24},{22,23}} [31](2, 0){{6,10},{6,10},{6,7},{7,22},{7,23},{10,20},{13,24},{13,19},{13,20},{19,21},{19,21},{20,24},{21,22},{22,23},{23,24}} [53](2, 0){{6,10},{6,10},{6,7},{7,22},{7,23},{10,17},{17,24},{17,23},{19,20},{19,21},{19,22},{20,24},{20,24},{21,22},{21,23}} [60](2, 0){{6,24},{6,23},{6,7},{7,20},{7,21},{10,18},{10,18},{10,20},{18,19},{19,22},{19,22},{20,21},{21,24},{22,23},{23,24}} [72](2, 0){{6,10},{6,10},{6,7},{7,19},{7,19},{10,17},{17,24},{17,22},{19,20},{20,24},{20,21},{21,22},{21,23},{22,23},{23,24}} [77](2, 0){{6,9},{6,18},{6,20},{9,16},{9,23},{16,18},{16,18},{17,24},{17,21},{17,22},{20,21},{20,21},{22,24},{22,23},{23,24}} [115](2, 0){{5,9},{5,10},{5,22},{8,20},{8,20},{8,23},{9,10},{9,22},{10,11},{11,12},{11,15},{12,15},{12,15},{20,23},{22,23}} [118](2, 0){{5,18},{5,22},{5,14},{8,17},{8,17},{8,23},{14,18},{14,19},{15,20},{15,20},{15,22},{17,23},{18,19},{19,20},{22,23}} [126](2, 0){{4,11},{4,11},{4,22},{11,14},{12,16},{12,18},{12,20},{14,17},{14,17},{16,20},{16,23},{17,18},{18,22},{20,23},{22,23}} [128](2, 0){{4,11},{4,11},{4,23},{11,14},{12,16},{12,19},{12,22},{14,17},{14,17},{16,19},{16,21},{17,23},{19,21},{21,22},{22,23}} [152](2, 0){{3,19},{3,5},{3,5},{5,6},{6,15},{6,7},{7,18},{7,14},{10,16},{10,16},{10,19},{14,18},{14,15},{15,16},{18,19}} There are 10 with 0 loops and 3 biedges: [9](3, 0){{6,9},{6,9},{6,23},{9,23},{10,11},{10,22},{10,22},{11,12},{11,15},{12,24},{12,15},{15,21},{21,24},{21,24},{22,23}} [20](3, 0){{6,10},{6,10},{6,7},{7,24},{7,11},{10,11},{11,22},{19,20},{19,21},{19,21},{20,24},{20,23},{21,24},{22,23},{22,23}} [29](3, 0){{6,10},{6,10},{6,7},{7,11},{7,12},{10,11},{11,12},{12,13},{13,24},{13,14},{14,22},{14,22},{22,23},{23,24},{23,24}} [33](3, 0){{6,9},{6,9},{6,20},{9,20},{17,18},{17,21},{17,21},{18,24},{18,23},{19,24},{19,20},{19,22},{21,24},{22,23},{22,23}} [38](3, 0){{6,10},{6,10},{6,7},{7,11},{7,23},{10,11},{11,22},{12,20},{12,20},{12,23},{20,21},{21,24},{21,24},{22,24},{22,23}} [43](3, 0){{6,9},{6,9},{6,21},{9,21},{10,18},{10,18},{10,23},{18,19},{19,24},{19,24},{20,21},{20,22},{20,23},{22,24},{22,23}} [44](3, 0){{6,10},{6,10},{6,7},{7,22},{7,23},{10,18},{11,20},{11,20},{11,22},{18,24},{18,23},{20,21},{21,24},{21,24},{22,23}} [59](3, 0){{6,8},{6,8},{6,18},{8,18},{16,20},{16,21},{16,21},{17,18},{17,19},{17,22},{19,20},{19,23},{20,21},{22,23},{22,23}} [87](3, 0){{6,10},{6,10},{6,7},{7,18},{7,18},{10,16},{16,20},{16,20},{18,19},{19,24},{19,22},{20,23},{22,24},{22,23},{23,24}} [107](3, 0){{2,16},{2,16},{2,20},{6,24},{6,12},{6,23},{12,21},{12,21},{16,19},{17,20},{17,23},{17,23},{19,24},{19,21},{20,24}} There are 6 with 0 loops and 4 biedges: [39](4, 0){{6,9},{6,9},{6,23},{9,23},{10,11},{10,22},{10,22},{11,24},{11,12},{12,20},{12,20},{20,21},{21,24},{21,24},{22,23}} [86](4, 0){{6,16},{6,23},{6,23},{7,18},{7,18},{7,21},{15,16},{15,22},{15,23},{16,24},{18,19},{19,24},{19,24},{21,22},{21,22}} [116](4, 0){{7,20},{7,20},{7,23},{8,16},{8,16},{8,9},{9,10},{9,13},{10,13},{10,13},{16,17},{17,22},{17,22},{20,23},{22,23}} [121](4, 0){{5,13},{5,13},{5,22},{8,18},{8,18},{8,23},{13,16},{15,20},{15,20},{15,22},{16,19},{16,19},{18,23},{19,20},{22,23}} [131](4, 0){{2,9},{2,9},{2,22},{9,11},{10,20},{10,20},{10,14},{11,13},{11,13},{13,14},{14,22},{20,21},{21,23},{21,23},{22,23}} [132](4, 0){{2,9},{2,9},{2,23},{9,11},{10,19},{10,19},{10,22},{11,13},{11,13},{13,23},{19,20},{20,21},{20,21},{21,22},{22,23}} There are 1 with 0 loops and 5 biedges: [109](5, 0){{6,10},{6,10},{6,7},{7,15},{7,15},{10,13},{13,20},{13,20},{15,19},{17,19},{17,19},{17,23},{20,24},{23,24},{23,24}} There are 65 graphs with 1 loops: There are 11 with 1 loops and 0 biedges: [13](0, 1){{6,24},{6,23},{6,7},{7,22},{7,21},{10,13},{10,14},{10,21},{13,14},{13,23},{14,15},{15,15},{21,22},{22,24},{23,24}} [28](0, 1){{6,24},{6,23},{6,7},{7,22},{7,21},{12,20},{12,13},{12,23},{13,21},{13,14},{14,14},{20,21},{20,22},{22,24},{23,24}} [30](0, 1){{6,21},{6,22},{6,7},{7,20},{7,23},{12,24},{12,13},{12,21},{13,20},{13,14},{14,14},{20,23},{21,22},{22,24},{23,24}} [35](0, 1){{6,24},{6,23},{6,7},{7,22},{7,21},{12,19},{12,13},{12,21},{13,13},{19,20},{19,21},{20,22},{20,23},{22,24},{23,24}} [45](0, 1){{6,23},{6,22},{6,7},{7,24},{7,20},{12,23},{12,13},{12,21},{13,20},{13,14},{14,14},{20,24},{21,22},{21,23},{22,24}} [56](0, 1){{3,18},{3,6},{3,7},{6,18},{6,7},{7,8},{8,9},{8,23},{9,24},{9,20},{18,19},{19,19},{20,24},{20,23},{23,24}} [66](0, 1){{8,9},{8,21},{8,23},{9,10},{9,22},{10,10},{17,24},{17,19},{17,20},{19,21},{19,22},{20,24},{20,23},{21,22},{23,24}} [73](0, 1){{3,16},{3,20},{3,6},{6,16},{6,19},{7,24},{7,18},{7,20},{16,17},{17,17},{18,24},{18,23},{19,20},{19,23},{23,24}} [104](0, 1){{2,20},{2,22},{2,15},{5,24},{5,19},{5,20},{15,16},{15,22},{16,17},{16,23},{17,17},{19,24},{19,23},{20,22},{23,24}} [147](0, 1){{9,17},{9,11},{9,12},{10,16},{10,13},{10,14},{11,16},{11,13},{12,18},{12,13},{14,17},{14,18},{16,17},{18,19},{19,19}} [149](0, 1){{9,10},{9,11},{9,15},{10,18},{10,14},{11,16},{11,19},{12,16},{12,19},{12,15},{14,18},{14,15},{16,17},{17,17},{18,19}} There are 19 with 1 loops and 1 biedges: [1](1, 1){{6,10},{6,10},{6,7},{7,11},{7,12},{10,11},{11,12},{12,13},{13,17},{13,14},{14,17},{14,18},{17,18},{18,19},{19,19}} [4](1, 1){{6,10},{6,10},{6,7},{7,24},{7,11},{10,11},{11,23},{12,24},{12,16},{12,15},{15,16},{15,23},{16,17},{17,17},{23,24}} [5](1, 1){{6,9},{6,9},{6,22},{9,22},{10,24},{10,13},{10,14},{13,14},{13,23},{14,15},{15,15},{21,24},{21,22},{21,23},{23,24}} [7](1, 1){{6,10},{6,10},{6,7},{7,24},{7,11},{10,11},{11,22},{14,23},{14,22},{14,15},{15,16},{15,24},{16,16},{22,23},{23,24}} [8](1, 1){{6,10},{6,10},{6,7},{7,24},{7,23},{10,22},{11,15},{11,14},{11,23},{14,22},{14,15},{15,16},{16,16},{22,24},{23,24}} [12](1, 1){{6,9},{6,9},{6,21},{9,21},{12,13},{12,22},{12,23},{13,24},{13,14},{14,14},{20,24},{20,21},{20,22},{22,23},{23,24}} [15](1, 1){{6,10},{6,10},{6,7},{7,24},{7,23},{10,21},{13,22},{13,14},{13,21},{14,23},{14,15},{15,15},{21,24},{22,24},{22,23}} [27](1, 1){{6,10},{6,10},{6,7},{7,22},{7,23},{10,21},{13,24},{13,21},{13,14},{14,22},{14,15},{15,15},{21,24},{22,23},{23,24}} [55](1, 1){{6,9},{6,10},{6,20},{9,10},{9,23},{10,11},{11,11},{18,24},{18,21},{18,22},{20,21},{20,21},{22,24},{22,23},{23,24}} [64](1, 1){{6,23},{6,22},{6,7},{7,20},{7,20},{11,24},{11,12},{11,22},{12,13},{12,21},{13,13},{20,21},{21,24},{22,23},{23,24}} [65](1, 1){{6,24},{6,23},{6,7},{7,18},{7,22},{11,19},{11,19},{11,12},{12,12},{18,19},{18,20},{20,22},{20,23},{22,24},{23,24}} [69](1, 1){{6,24},{6,23},{6,7},{7,20},{7,20},{11,24},{11,12},{11,22},{12,13},{12,21},{13,13},{20,21},{21,23},{22,24},{22,23}} [78](1, 1){{6,23},{6,21},{6,7},{7,24},{7,22},{11,19},{11,19},{11,12},{12,13},{12,22},{13,13},{19,21},{21,23},{22,24},{23,24}} [79](1, 1){{5,24},{5,18},{5,20},{14,17},{14,17},{14,15},{15,15},{16,17},{16,19},{16,20},{18,24},{18,23},{19,20},{19,23},{23,24}} [97](1, 1){{7,8},{7,24},{7,22},{8,9},{8,21},{9,9},{16,24},{16,18},{16,19},{18,21},{18,21},{19,22},{19,23},{22,23},{23,24}} [100](1, 1){{6,22},{6,22},{6,14},{13,22},{13,21},{13,14},{14,17},{16,24},{16,17},{16,23},{17,18},{18,18},{21,24},{21,23},{23,24}} [122](1, 1){{3,19},{3,11},{3,14},{8,11},{8,12},{8,15},{11,14},{12,19},{12,15},{14,15},{19,20},{20,22},{20,22},{22,23},{23,23}} [129](1, 1){{10,16},{10,19},{10,13},{12,20},{12,15},{12,15},{13,19},{13,23},{15,16},{16,22},{19,23},{20,21},{20,22},{21,21},{22,23}} [130](1, 1){{10,18},{10,13},{10,22},{12,19},{12,15},{12,15},{13,18},{13,21},{15,23},{18,21},{19,20},{19,23},{20,20},{21,22},{22,23}} There are 21 with 1 loops and 2 biedges: [2](2, 1){{6,24},{6,9},{6,9},{9,24},{10,11},{10,23},{10,23},{11,12},{11,15},{12,16},{12,15},{15,16},{16,17},{17,17},{23,24}} [18](2, 1){{6,10},{6,10},{6,7},{7,24},{7,11},{10,11},{11,22},{14,24},{14,21},{14,15},{15,15},{21,24},{21,23},{22,23},{22,23}} [19](2, 1){{6,9},{6,9},{6,21},{9,21},{12,24},{12,19},{12,13},{13,13},{19,24},{19,23},{20,24},{20,21},{20,22},{22,23},{22,23}} [46](2, 1){{6,10},{6,10},{6,7},{7,22},{7,22},{10,20},{12,24},{12,20},{12,13},{13,14},{13,23},{14,14},{20,24},{22,23},{23,24}} [48](2, 1){{6,9},{6,9},{6,7},{7,24},{7,20},{9,19},{12,13},{12,21},{12,21},{13,13},{19,24},{19,22},{20,21},{20,22},{22,24}} [49](2, 1){{6,10},{6,10},{6,7},{7,11},{7,12},{10,11},{11,12},{12,13},{13,22},{13,14},{14,21},{14,21},{21,22},{22,23},{23,23}} [63](2, 1){{6,10},{6,10},{6,7},{7,24},{7,11},{10,11},{11,23},{12,24},{12,19},{12,19},{19,20},{20,21},{20,23},{21,21},{23,24}} [67](2, 1){{5,18},{5,18},{5,6},{6,23},{6,7},{7,24},{7,20},{16,17},{16,19},{16,19},{17,17},{18,19},{20,24},{20,23},{23,24}} [70](2, 1){{5,8},{5,20},{5,22},{8,14},{8,21},{14,20},{14,20},{16,17},{16,19},{16,19},{17,17},{18,19},{18,21},{18,22},{21,22}} [74](2, 1){{6,9},{6,9},{6,22},{9,22},{10,24},{10,17},{10,17},{17,18},{18,19},{18,23},{19,19},{21,24},{21,22},{21,23},{23,24}} [75](2, 1){{6,10},{6,10},{6,7},{7,24},{7,23},{10,17},{11,19},{11,19},{11,23},{17,24},{17,20},{19,20},{20,21},{21,21},{23,24}} [81](2, 1){{3,17},{3,6},{3,7},{6,17},{6,7},{7,8},{8,24},{8,9},{9,20},{9,20},{17,18},{18,18},{20,21},{21,24},{21,24}} [84](2, 1){{3,21},{3,6},{3,15},{6,20},{6,15},{7,18},{7,18},{7,21},{15,16},{16,16},{18,19},{19,24},{19,24},{20,24},{20,21}} [90](2, 1){{5,17},{5,21},{5,21},{8,24},{8,9},{8,17},{9,10},{9,23},{10,10},{17,24},{18,24},{18,20},{18,21},{20,23},{20,23}} [103](2, 1){{6,20},{6,15},{6,15},{13,24},{13,21},{13,22},{15,16},{16,17},{16,23},{17,17},{20,21},{20,21},{22,24},{22,23},{23,24}} [105](2, 1){{2,17},{2,17},{2,21},{6,24},{6,23},{6,7},{7,8},{7,20},{8,8},{17,20},{18,21},{18,23},{18,23},{20,24},{21,24}} [108](2, 1){{6,15},{6,15},{6,7},{7,8},{7,23},{8,8},{15,21},{17,24},{17,19},{17,20},{19,23},{19,23},{20,24},{20,21},{21,24}} [119](2, 1){{3,19},{3,6},{3,7},{6,19},{6,7},{7,8},{8,9},{8,12},{9,12},{9,12},{19,20},{20,22},{20,22},{22,23},{23,23}} [123](2, 1){{3,10},{3,19},{3,13},{10,13},{10,15},{11,16},{11,16},{11,19},{13,15},{15,16},{19,20},{20,22},{20,22},{22,23},{23,23}} [141](2, 1){{3,6},{3,6},{3,7},{6,7},{7,8},{8,9},{8,19},{9,17},{9,10},{10,15},{10,15},{15,17},{17,19},{18,18},{18,19}} [144](2, 1){{3,13},{3,6},{3,6},{6,12},{7,8},{7,17},{7,13},{8,15},{8,15},{12,19},{12,13},{15,17},{17,19},{18,18},{18,19}} There are 10 with 1 loops and 3 biedges: [37](3, 1){{6,9},{6,9},{6,7},{7,10},{7,20},{9,10},{10,22},{13,21},{13,21},{13,14},{14,14},{20,23},{20,21},{22,23},{22,23}} [51](3, 1){{6,8},{6,8},{6,19},{8,19},{11,12},{11,21},{11,21},{12,12},{18,19},{18,20},{18,22},{20,21},{20,23},{22,23},{22,23}} [57](3, 1){{5,20},{5,20},{5,6},{6,10},{6,7},{7,10},{7,22},{10,16},{16,22},{16,22},{18,19},{18,21},{18,21},{19,19},{20,21}} [58](3, 1){{6,24},{6,9},{6,9},{9,24},{10,11},{10,23},{10,23},{11,20},{11,12},{12,19},{12,19},{19,20},{20,21},{21,21},{23,24}} [91](3, 1){{5,16},{5,16},{5,21},{13,19},{13,19},{13,14},{14,14},{16,17},{17,24},{17,24},{18,19},{18,20},{18,21},{20,24},{20,21}} [95](3, 1){{6,24},{6,24},{6,15},{7,17},{7,17},{7,22},{14,24},{14,23},{14,15},{15,18},{17,18},{18,19},{19,19},{22,23},{22,23}} [96](3, 1){{4,8},{4,22},{4,7},{7,8},{7,24},{8,9},{9,9},{16,21},{16,21},{16,23},{19,24},{19,24},{19,21},{22,23},{22,23}} [133](3, 1){{9,20},{9,20},{9,14},{10,17},{10,13},{10,13},{13,14},{14,22},{17,18},{17,22},{18,18},{20,21},{21,23},{21,23},{22,23}} [134](3, 1){{9,19},{9,19},{9,22},{10,16},{10,13},{10,13},{13,23},{16,17},{16,23},{17,17},{19,20},{20,21},{20,21},{21,22},{22,23}} [148](3, 1){{5,10},{5,19},{5,6},{6,15},{6,15},{10,13},{10,13},{12,16},{12,18},{12,18},{13,16},{15,19},{16,17},{17,17},{18,19}} There are 4 with 1 loops and 4 biedges: [85](4, 1){{5,20},{5,20},{5,6},{6,24},{6,7},{7,18},{7,18},{15,16},{15,21},{15,21},{16,16},{18,19},{19,24},{19,24},{20,21}} [111](4, 1){{4,22},{4,15},{4,15},{11,21},{11,21},{11,23},{15,16},{16,24},{16,17},{17,17},{19,24},{19,24},{19,21},{22,23},{22,23}} [120](4, 1){{5,13},{5,13},{5,6},{6,10},{6,7},{7,10},{7,10},{13,14},{14,19},{14,19},{19,20},{20,22},{20,22},{22,23},{23,23}} [127](4, 1){{3,10},{3,10},{3,19},{10,12},{11,16},{11,16},{11,19},{12,15},{12,15},{15,16},{19,20},{20,22},{20,22},{22,23},{23,23}} There are 28 graphs with 2 loops: There are 7 with 2 loops and 0 biedges: [36](0, 2){{3,21},{3,6},{3,7},{6,21},{6,7},{7,8},{8,9},{8,12},{9,12},{9,13},{12,13},{13,14},{14,14},{21,22},{22,22}} [47](0, 2){{3,19},{3,22},{3,6},{6,19},{6,21},{7,10},{7,11},{7,22},{10,11},{10,21},{11,12},{12,12},{19,20},{20,20},{21,22}} [52](0, 2){{3,24},{3,18},{3,6},{6,18},{6,20},{9,10},{9,20},{9,23},{10,24},{10,11},{11,11},{18,19},{19,19},{20,23},{23,24}} [71](0, 2){{3,24},{3,18},{3,23},{8,9},{8,22},{8,17},{9,10},{9,23},{10,10},{17,24},{17,18},{18,19},{19,19},{22,24},{22,23}} [80](0, 2){{3,18},{3,22},{3,23},{8,24},{8,9},{8,17},{9,10},{9,22},{10,10},{17,24},{17,18},{18,19},{19,19},{22,23},{23,24}} [98](0, 2){{2,24},{2,18},{2,22},{5,8},{5,22},{5,7},{7,8},{7,19},{8,9},{9,9},{18,24},{18,19},{19,20},{20,20},{22,24}} [99](0, 2){{2,24},{2,17},{2,23},{6,18},{6,22},{6,7},{7,8},{7,23},{8,8},{17,24},{17,18},{18,19},{19,19},{22,24},{22,23}} There are 10 with 2 loops and 1 biedges: [54](1, 2){{5,8},{5,9},{5,22},{8,9},{8,21},{9,10},{10,10},{17,18},{17,20},{17,20},{18,18},{19,20},{19,21},{19,22},{21,22}} [68](1, 2){{7,8},{7,20},{7,23},{8,24},{8,9},{9,9},{16,17},{16,19},{16,19},{17,17},{18,24},{18,19},{18,20},{20,23},{23,24}} [76](1, 2){{3,24},{3,18},{3,6},{6,18},{6,20},{9,16},{9,24},{9,10},{10,10},{16,24},{16,21},{18,19},{19,19},{20,21},{20,21}} [88](1, 2){{3,16},{3,6},{3,7},{6,16},{6,7},{7,8},{8,9},{8,20},{9,19},{9,19},{16,17},{17,17},{19,20},{20,21},{21,21}} [92](1, 2){{3,17},{3,20},{3,20},{7,8},{7,24},{7,16},{8,9},{8,21},{9,9},{16,24},{16,17},{17,18},{18,18},{20,21},{21,24}} [94](1, 2){{3,14},{3,22},{3,6},{6,21},{6,14},{7,17},{7,17},{7,22},{14,15},{15,15},{17,18},{18,19},{18,21},{19,19},{21,22}} [102](1, 2){{3,24},{3,21},{3,14},{6,17},{6,17},{6,21},{13,24},{13,18},{13,14},{14,15},{15,15},{17,18},{18,19},{19,19},{21,24}} [110](1, 2){{2,16},{2,16},{2,19},{5,24},{5,20},{5,6},{6,18},{6,7},{7,7},{16,18},{18,24},{19,24},{19,20},{20,21},{21,21}} [145](1, 2){{3,6},{3,6},{3,7},{6,7},{7,8},{8,9},{8,19},{9,16},{9,17},{15,16},{15,15},{16,17},{17,19},{18,18},{18,19}} [146](1, 2){{3,12},{3,6},{3,6},{6,11},{7,16},{7,17},{7,12},{11,19},{11,12},{15,16},{15,15},{16,17},{17,19},{18,18},{18,19}} There are 8 with 2 loops and 2 biedges: [50](2, 2){{5,21},{5,21},{5,6},{6,10},{6,7},{7,10},{7,11},{10,11},{11,12},{12,12},{19,20},{19,22},{19,22},{20,20},{21,22}} [82](2, 2){{7,8},{7,24},{7,14},{8,8},{14,24},{14,21},{16,17},{16,19},{16,19},{17,17},{18,24},{18,19},{18,20},{20,21},{20,21}} [101](2, 2){{5,22},{5,15},{5,15},{12,20},{12,20},{12,13},{13,13},{15,16},{16,17},{16,21},{17,17},{19,20},{19,21},{19,22},{21,22}} [106](2, 2){{4,7},{4,6},{4,23},{6,20},{6,7},{7,8},{8,8},{15,24},{15,19},{15,19},{19,20},{20,21},{21,21},{23,24},{23,24}} [135](2, 2){{8,16},{8,12},{8,12},{12,13},{13,20},{13,22},{16,17},{16,20},{17,17},{19,21},{19,21},{19,22},{20,21},{22,23},{23,23}} [136](2, 2){{8,12},{8,12},{8,15},{12,21},{15,16},{15,21},{16,16},{18,19},{18,19},{18,22},{19,20},{20,21},{20,22},{22,23},{23,23}} [137](2, 2){{6,22},{6,22},{6,7},{7,8},{7,11},{8,11},{8,12},{11,12},{12,13},{13,21},{13,21},{20,20},{20,21},{22,23},{23,23}} [150](2, 2){{5,9},{5,19},{5,17},{9,12},{9,12},{11,18},{11,18},{11,14},{12,14},{14,15},{15,15},{16,16},{16,17},{17,19},{18,19}} There are 2 with 2 loops and 3 biedges: [89](3, 2){{6,19},{6,19},{6,7},{7,7},{14,17},{14,17},{14,15},{15,15},{16,17},{16,18},{16,20},{18,19},{18,21},{20,21},{20,21}} [93](3, 2){{5,21},{5,21},{5,6},{6,18},{6,7},{7,17},{7,17},{14,22},{14,22},{14,15},{15,15},{17,18},{18,19},{19,19},{21,22}} There are 1 with 2 loops and 4 biedges: [138](4, 2){{6,22},{6,22},{6,7},{7,19},{7,19},{10,18},{10,18},{10,11},{11,21},{11,21},{18,19},{20,20},{20,21},{22,23},{23,23}} There are 1 graphs with 3 loops: There are 1 with 3 loops and 0 biedges: [112](0, 3){{4,24},{4,5},{4,21},{5,16},{5,6},{6,6},{16,24},{16,17},{17,18},{17,20},{18,18},{20,24},{20,21},{21,22},{22,22}}