K-regular simple graphs with N nodes N = 3 K = 2 1 solution (69 inferences) [1-2, 1-3, 2-3] N = 4 K = 2 1 solution (95 inferences) [1-2, 1-3, 2-4, 3-4] N = 4 K = 3 1 solution (124 inferences) [1-2, 1-3, 1-4, 2-3, 2-4, 3-4] N = 5 K = 2 1 solution (339 inferences) [1-2, 1-3, 2-4, 3-5, 4-5] N = 5 K = 3 0 solution (261 inferences) N = 5 K = 4 1 solution (251 inferences) [1-2, 1-3, 1-4, 1-5, 2-3, 2-4, 2-5, 3-4, 3-5, 4-5] N = 6 K = 2 2 solutions (21198 inferences) [1-2, 1-3, 2-3, 4-5, 4-6, 5-6] [1-2, 1-3, 2-4, 3-5, 4-6, 5-6] N = 6 K = 3 2 solutions (38662 inferences) [1-2, 1-3, 1-4, 2-3, 2-5, 3-6, 4-5, 4-6, 5-6] [1-2, 1-3, 1-4, 2-5, 2-6, 3-5, 3-6, 4-5, 4-6] N = 6 K = 4 1 solution (4698 inferences) [1-2, 1-3, 1-4, 1-5, 2-3, 2-4, 2-6, 3-5, 3-6, 4-5, 4-6, 5-6] N = 6 K = 5 1 solution (546 inferences) [1-2, 1-3, 1-4, 1-5, 1-6, 2-3, 2-4, 2-5, 2-6, 3-4, 3-5, 3-6, 4-5, 4-6, 5-6] N = 7 K = 2 2 solutions (150137 inferences) [1-2, 1-3, 2-3, 4-5, 4-6, 5-7, 6-7] [1-2, 1-3, 2-4, 3-5, 4-6, 5-7, 6-7] N = 7 K = 3 0 solution (7693 inferences) N = 7 K = 4 2 solutions (4088301 inferences) [1-2, 1-3, 1-4, 1-5, 2-3, 2-4, 2-5, 3-6, 3-7, 4-6, 4-7, 5-6, 5-7, 6-7] [1-2, 1-3, 1-4, 1-5, 2-3, 2-4, 2-6, 3-5, 3-7, 4-6, 4-7, 5-6, 5-7, 6-7] N = 7 K = 5 0 solution (4849 inferences) N = 7 K = 6 1 solution (1225 inferences) [1-2, 1-3, 1-4, 1-5, 1-6, 1-7, 2-3, 2-4, 2-5, 2-6, 2-7, 3-4, 3-5, 3-6, 3-7, 4-5, 4-6, 4-7, 5-6, 5-7, 6-7] N = 8 K = 2 3 solutions (2762047 inferences) [1-2, 1-3, 2-3, 4-5, 4-6, 5-7, 6-8, 7-8] [1-2, 1-3, 2-4, 3-4, 5-6, 5-7, 6-8, 7-8] [1-2, 1-3, 2-4, 3-5, 4-6, 5-7, 6-8, 7-8] N = 8 K = 3 6 solutions (67636365 inferences) [1-2, 1-3, 1-4, 2-3, 2-4, 3-4, 5-6, 5-7, 5-8, 6-7, 6-8, 7-8] [1-2, 1-3, 1-4, 2-3, 2-4, 3-5, 4-6, 5-7, 5-8, 6-7, 6-8, 7-8] [1-2, 1-3, 1-4, 2-3, 2-5, 3-6, 4-5, 4-7, 5-8, 6-7, 6-8, 7-8] [1-2, 1-3, 1-4, 2-3, 2-5, 3-6, 4-7, 4-8, 5-7, 5-8, 6-7, 6-8] [1-2, 1-3, 1-4, 2-5, 2-6, 3-5, 3-7, 4-6, 4-7, 5-8, 6-8, 7-8] [1-2, 1-3, 1-4, 2-5, 2-6, 3-5, 3-7, 4-6, 4-8, 5-8, 6-7, 7-8] N = 8 K = 4 6 solutions (338976076 inferences) [1-2, 1-3, 1-4, 1-5, 2-3, 2-4, 2-5, 3-6, 3-7, 4-6, 4-8, 5-7, 5-8, 6-7, 6-8, 7-8] [1-2, 1-3, 1-4, 1-5, 2-3, 2-4, 2-6, 3-4, 3-7, 4-8, 5-6, 5-7, 5-8, 6-7, 6-8, 7-8] [1-2, 1-3, 1-4, 1-5, 2-3, 2-4, 2-6, 3-5, 3-7, 4-6, 4-8, 5-7, 5-8, 6-7, 6-8, 7-8] [1-2, 1-3, 1-4, 1-5, 2-3, 2-4, 2-6, 3-5, 3-7, 4-7, 4-8, 5-6, 5-8, 6-7, 6-8, 7-8] [1-2, 1-3, 1-4, 1-5, 2-3, 2-4, 2-6, 3-7, 3-8, 4-7, 4-8, 5-6, 5-7, 5-8, 6-7, 6-8] [1-2, 1-3, 1-4, 1-5, 2-6, 2-7, 2-8, 3-6, 3-7, 3-8, 4-6, 4-7, 4-8, 5-6, 5-7, 5-8] N = 8 K = 5 3 solutions (259887137 inferences) [1-2, 1-3, 1-4, 1-5, 1-6, 2-3, 2-4, 2-5, 2-6, 3-4, 3-7, 3-8, 4-7, 4-8, 5-6, 5-7, 5-8, 6-7, 6-8, 7-8] [1-2, 1-3, 1-4, 1-5, 1-6, 2-3, 2-4, 2-5, 2-7, 3-4, 3-6, 3-8, 4-7, 4-8, 5-6, 5-7, 5-8, 6-7, 6-8, 7-8] [1-2, 1-3, 1-4, 1-5, 1-6, 2-3, 2-4, 2-5, 2-7, 3-6, 3-7, 3-8, 4-6, 4-7, 4-8, 5-6, 5-7, 5-8, 6-8, 7-8] N = 8 K = 6 1 solution (742954 inferences) [1-2, 1-3, 1-4, 1-5, 1-6, 1-7, 2-3, 2-4, 2-5, 2-6, 2-8, 3-4, 3-5, 3-7, 3-8, 4-6, 4-7, 4-8, 5-6, 5-7, 5-8, 6-7, 6-8, 7-8] N = 8 K = 7 1 solution (2768 inferences) [1-2, 1-3, 1-4, 1-5, 1-6, 1-7, 1-8, 2-3, 2-4, 2-5, 2-6, 2-7, 2-8, 3-4, 3-5, 3-6, 3-7, 3-8, 4-5, 4-6, 4-7, 4-8, 5-6, 5-7, 5-8, 6-7, 6-8, 7-8] N = 9 K = 2 4 solutions (54627139 inferences) [1-2, 1-3, 2-3, 4-5, 4-6, 5-6, 7-8, 7-9, 8-9] [1-2, 1-3, 2-3, 4-5, 4-6, 5-7, 6-8, 7-9, 8-9] [1-2, 1-3, 2-4, 3-4, 5-6, 5-7, 6-8, 7-9, 8-9] [1-2, 1-3, 2-4, 3-5, 4-6, 5-7, 6-8, 7-9, 8-9]