The genus for various cage graphs using the adjacency lists from win.tue.nl. Number (# links to adjacency list), valency (k), girth (g), vertices (v), edges (e), size of the automorphism group (|G|), genus, computation time for the genus (time), computation time for the genus using SageMath (SM time), and computation time using multi_genus.c (MG time).
| # | k | g | v | e | |G| | genus | time (s) | SM time (s) | MG time (s) |
|---|---|---|---|---|---|---|---|---|---|
| 1/1 | 3 | 3 | 4 | 6 | 24 | 0 | 0.004 | 0.004 | 0.006 |
| 1/1 | 3 | 4 | 6 | 9 | 72 | 1 | 0.003 | 0.039 | 0.006 |
| 1/1 | 3 | 5 | 10 | 15 | 120 | 1 | 0.005 | 0.027 | 0.006 |
| 1/1 | 3 | 6 | 14 | 21 | 336 | 1 | 0.005 | 0.010 | 0.006 |
| 1/1 | 3 | 7 | 24 | 36 | 32 | 2 | 0.005 | 1.737 | 0.006 |
| 1/1 | 3 | 8 | 30 | 45 | 1440 | 4 | 0.016 | 118.958 | 0.012 |
| 1/18 | 3 | 9 | 58 | 87 | 4 | 7 | 0.222 | days | 29.084 |
| 2/18 | 3 | 9 | 58 | 87 | 2 | 7 | 1.018 | days | 30.909 |
| 3/18 | 3 | 9 | 58 | 87 | 24 | 7 | 1.851 | days | 25.993 |
| 4/18 | 3 | 9 | 58 | 87 | 4 | 7 | 0.301 | days | 54.396 |
| 5/18 | 3 | 9 | 58 | 87 | 4 | 7 | 0.380 | days | 67.89 |
| 6/18 | 3 | 9 | 58 | 87 | 2 | 7 | 0.330 | days | 45.310 |
| 7/18 | 3 | 9 | 58 | 87 | 1 | 7 | 0.639 | days | 37.257 |
| 8/18 | 3 | 9 | 58 | 87 | 2 | 7 | 1.024 | days | 42.843 |
| 9/18 | 3 | 9 | 58 | 87 | 1 | 7 | 0.903 | days | 34.437 |
| 10/18 | 3 | 9 | 58 | 87 | 2 | 7 | 0.215 | days | 86.54 |
| 11/18 | 3 | 9 | 58 | 87 | 1 | 7 | 0.204 | days | 54.990 |
| 12/18 | 3 | 9 | 58 | 87 | 2 | 7 | 1.273 | days | 51.589 |
| 13/18 | 3 | 9 | 58 | 87 | 1 | 7 | 0.839 | days | 32.340 |
| 14/18 | 3 | 9 | 58 | 87 | 12 | 7 | 1.056 | days | 30.824 |
| 15/18 | 3 | 9 | 58 | 87 | 8 | 7 | 0.530 | days | 44.888 |
| 16/18 | 3 | 9 | 58 | 87 | 2 | 7 | 0.208 | days | 57.890 |
| 17/18 | 3 | 9 | 58 | 87 | 6 | 7 | 0.879 | days | 140.50 |
| 18/18 | 3 | 9 | 58 | 87 | 6 | 7 | 0.849 | days | 47.737 |
| 1/3 | 3 | 10 | 70 | 105 | 120 | 9 | 0.547 | DNF | 9354.14 |
| 2/3 | 3 | 10 | 70 | 105 | 24 | 9 | 0.694 | DNF | 9556.13 |
| 3/3 | 3 | 10 | 70 | 105 | 80 | 9 | 0.418 | DNF | 10680.89 |
| 1/1 | 3 | 11 | 112 | 168 | 64 | [15, 17] | days | DNF | days |
| 1/1 | 3 | 12 | 126 | 189 | 12096 | 17 | 0.427 | DNF | days |
| 1/1 | 4 | 5 | 19 | 38 | 24 | 4 | 0.064 | days | 0.019 |
| 1/1 | 4 | 6 | 26 | 52 | 11232 | 6 | 0.016 | DNF | 0.013 |
| 1/? | 4 | 7 | 67 | 134 | 4 | [16, 21] | days | DNF | days |
| 1/1 | 4 | 8 | 80 | 160 | 51840 | [21, 27] | days | DNF | days |
| 1/? | 4 | 12 | 728 | 1456 | 8491392 | [244, 363] | DNF | DNF | too big for bit operations |
| 1/4 | 5 | 5 | 30 | 75 | 120 | [9, 10] | days | DNF | days |
| 2/4 | 5 | 5 | 30 | 75 | 20 | [9, 13] | days | DNF | days |
| 3/4 | 5 | 5 | 30 | 75 | 30 | [9, 14] | days | DNF | days |
| 4/4 | 5 | 5 | 30 | 75 | 96 | [9, 14] | days | DNF | days |
| 1/1 | 5 | 6 | 42 | 105 | 241920 | [15, 17] | days | DNF | days |
| 1/1 | 5 | 8 | 170 | 425 | 3916800 | [76, 126] | DNF | DNF | too big for bit operations |
| 1/? | 5 | 12 | 2730 | 6825 | 503193600 | [1480, 2048] | OOM | DNF | too big for bit operations |
| 1/1 | 6 | 5 | 40 | 120 | 480 | [17, 22] | days | DNF | days |
| 1/1 | 6 | 6 | 62 | 186 | 744000 | [32, 60] | DNF | DNF | DNF |
| 1/1 | 6 | 8 | 312 | 936 | 9360000 | [196, 310] | DNF | DNF | too big for bit operations |
| 1/? | 6 | 12 | 7812 | 23436 | 5859000000 | [5860, 7810] | OOM | DNF | too big for bit operations |
| 1/1 | 7 | 5 | 50 | 175 | 252000 | [29, 39] | DNF | DNF | DNF |
| 1/1 | 7 | 6 | 90 | 315 | 15120 | [61, 110] | DNF | DNF | DNF |
The genus for various complete graphs generated using the CompleteGraph function in SageMath follows.
| # | k | g | v | e | |G| | genus | time (s) | SM time (s) | MG time (s) |
|---|---|---|---|---|---|---|---|---|---|
| k2 | 1 | Inf | 2 | 1 | 2 | 0 | --- | 0.004 | --- |
| k3 | 2 | 3 | 3 | 3 | 6 | 0 | 0.004 | 0.004 | 0.008 |
| k4 | 3 | 3 | 4 | 6 | 24 | 0 | 0.004 | 0.003 | 0.008 |
| k5 | 4 | 3 | 5 | 10 | 120 | 1 | 0.004 | 0.005 | 0.008 |
| k6 | 5 | 3 | 6 | 15 | 720 | 1 | 0.004 | 0.023 | 0.008 |
| k7 | 6 | 3 | 7 | 21 | 5040 | 1 | 0.004 | days | 0.009 |
| k8 | 7 | 3 | 8 | 28 | 40320 | 2 | 0.004 | DNF | 0.008 |
| k9 | 8 | 3 | 9 | 36 | 362880 | 3 | 0.004 | DNF | 0.008 |
The genus for various complete bipartite graphs generated using the CompleteBipartiteGraph function in SageMath follows. Number (# links to adjacency list), valency (k), girth (g), vertices (v), edges (e), size of the automorphism group (|G|), genus, computation time for the genus (time), and computation time for the genus using SageMath (SM time).
| # | k | g | v | e | |G| | genus | time (s) | SM time (s) | MG time (s) |
|---|---|---|---|---|---|---|---|---|---|
| k3-3 | 3 | 4 | 6 | 9 | 72 | 1 | 0.004 | 0.047 | 0.006 |
| k4-4 | 4 | 4 | 8 | 16 | 1152 | 1 | 0.004 | 0.010 | 0.010 |
| k5-5 | 5 | 4 | 10 | 25 | 28800 | 3 | 0.008 | DNF | 0.008 |
| k6-6 | 6 | 4 | 12 | 36 | 1036800 | 4 | 0.005 | DNF | 0.009 |
The genus for various complete n-partite graphs generated using the CompleteMultipartiteGraph function in SageMath follows.
| # | v | e | genus | time (s) | MG time (s) |
|---|---|---|---|---|---|
| k2-2 | 4 | 4 | 0 | 0.004 | 0.008 |
| k2-2-2 | 6 | 12 | 0 | 0.004 | 0.009 |
| k2-2-2-2 | 8 | 24 | 1 | 0.004 | 0.009 |
| k2-2-2-2-2 | 10 | 40 | 3 | 0.006 | 0.009 |
The genus for various Johnson graphs generated using Mathematica follows.
| # | v | e | genus | time (s) | MG time (s) |
|---|---|---|---|---|---|
| Johnson (5, 2) | 10 | 30 | 2 | 0.004 | 0.009 |
| Johnson (6, 2) | 15 | 60 | 5 | 23.101 | hours |
| Johnson (6, 3) | 20 | 90 | 7 | 19.374 | hours |
| Johnson (8, 4) | 70 | 560 | [60,238] | days | too big for bit operations |
| Johnson (9, 4) | 70 | 560 | [148,558] | days | too big for bit operations |
The genus for various Circulant graphs generated using Mathematica follows.
| # | v | e | genus | time (s) | MG time (s) |
|---|---|---|---|---|---|
| C10_1,2,5 | 10 | 25 | 1 | 0.005 | 0.007 |
| C10_1,2,4,5 | 10 | 35 | 3 | 0.009 | 0.023 |
| C14_1,2,3,6 | 14 | 48 | 4 | 0.013 | 0.896 |
| C15_1,5 | 15 | 30 | 1 | 0.008 | 0.006 |
| C16_1,7 | 16 | 32 | 1 | 0.005 | 0.014 |
| C18_1,3,9 | 18 | 45 | 4 | 0.579 | 0.021 |
| C20_1,3,5 | 20 | 60 | 6 | 0.010 | 13.698 |
| C20_1,6,9 | 20 | 60 | 6 | 0.009 | 20.637 |
| C21_1,4,5 | 21 | 63 | 1 | 0.011 | 0.008 |
| C26_1,3,9 | 26 | 78 | [8, 27] | hours | hours |
| C30_1,9,11 | 30 | 90 | [9, 31] | hours | hours |
| C30_1,4,11,14 | 30 | 120 | [16, 20] | hours | hours |
| C31_1,5,6 | 31 | 93 | 1 | 0.021 | 0.006 |
| C20_* | 20 | 110 | [10, 17] | hours | hours |
The genus for various Cyclotomic graphs generated using Mathematica follows.
| # | v | e | genus | time (s) | MG time (s) |
|---|---|---|---|---|---|
| 16 | 16 | 40 | 4 | 0.117 | 0.042 |
| 19 | 19 | 57 | 1 | 0.009 | 0.010 |
| 31 | 31 | 155 | [12,58] | hours | hours |
| 61 | 61 | 610 | [73,265] | days | too big for bit operations |
| 67 | 67 | 737 | [91,325] | days | too big for bit operations |
The genus for various DifferenceSetIncidence graphs generated using Mathematica follows.
| # | v | e | genus | time (s) | MG time (s) |
|---|---|---|---|---|---|
| 11,5,2 | 22 | 55 | 5 | 0.914 | 1.770 |
| 40,13,4 | 80 | 520 | [91,214] | hours | too big for bit operations |
The genus for various Bipartite Kneser graphs generated using Mathematica follows.
| # | v | e | genus | time (s) | MG time (s) |
|---|---|---|---|---|---|
| Bipartite Kneser (6, 2) | 30 | 90 | [9,28] | days | days |
| Bipartite Kneser (7, 2) | 42 | 210 | [33,80] | days | days |
| Bipartite Kneser (8, 2) | 56 | 420 | [78,175] | days | days |
| Bipartite Kneser (8, 3) | 112 | 560 | [85,143] | days | too big for bit operations |
| Bipartite Kneser (9, 2) | 72 | 756 | [154,332] | days | too big for bit operations |
| Bipartite Kneser (9, 3) | 168 | 1680 | [337,338] | days | too big for bit operations |
| Bipartite Kneser (10, 2) | 90 | 1260 | [271,572] | days | too big for bit operations |
| Bipartite Kneser (10, 3) | 240 | 4200 | [931,1963] | days | too big for bit operations |
| Bipartite Kneser (10, 4) | 420 | 3150 | [579,1358] | days | too big for bit operations |
| Bipartite Kneser (11, 2) | 110 | 1980 | [441,918] | days | too big for bit operations |
| Bipartite Kneser (11, 3) | 330 | 9240 | [2146,4428] | days | too big for bit operations |
| Bipartite Kneser (11, 4) | 660 | 11550 | [2558,5428] | days | too big for bit operations |
| Bipartite Kneser (12, 2) | 132 | 2970 | [677,1397] | days | too big for bit operations |
| Bipartite Kneser (12, 3) | 440 | 18480 | [4401,8979] | days | too big for bit operations |
| Bipartite Kneser (12, 4) | 990 | 34650 | ? | adjacency list too large to load | too big for bit operations |
The genus for various miscellaneous graphs generated using Mathematica follows.
| # | v | e | genus | time (s) | MG time (s) |
|---|---|---|---|---|---|
| Klein Bottle | 9 | 27 | 2 | 0.005 | 0.006 |
| TRC | 84 | 126 | 3 | hours | 0.006 |
| Fan (3, 6) | 9 | 23 | 1 | 0.004 | 0.006 |
| Co-Herschel | 11 | 37 | 2 | 0.004 | 0.006 |