n | #graphs | #char. pols | #graphs with mate | maxsz |
0 | 1 | 1 | 0 | 1 |
1 | 1 | 1 | 0 | 1 |
2 | 2 | 2 | 0 | 1 |
3 | 4 | 4 | 0 | 1 |
4 | 11 | 11 | 0 | 1 |
5 | 34 | 34 | 0 | 1 |
6 | 156 | 154 | 4 | 2 |
7 | 1044 | 976 | 130 | 3 |
8 | 12346 | 11398 | 1767 | 6 |
9 | 274668 | 251802 | 42595 | 9 |
10 | 12005168 | 11249513 | 1412438 | 23 |
11 | 1018997864 | 970760558 | 91274836 | 33 |
12 | 165091172592 | 159955412426 | 9854131240 | 226 |
In what follows below e denotes the number of edges, #cp the number of distinct characteristic polynomials and maxsz is the maximum number of graphs that have a cospectral mate.
n=4 n=5 n=6 n=7 n=8 n=9 n=10 n=11 n=12
e | #graphs | #cp | with mate | maxsz |
0 | 1 | 1 | 0 | 1 |
1 | 1 | 1 | 0 | 1 |
2 | 2 | 2 | 0 | 1 |
3 | 3 | 3 | 0 | 1 |
4 | 2 | 2 | 0 | 1 |
5 | 1 | 1 | 0 | 1 |
6 | 1 | 1 | 0 | 1 |
e | #graphs | #cp | with mate | maxsz |
0 | 1 | 1 | 0 | 1 |
1 | 1 | 1 | 0 | 1 |
2 | 2 | 2 | 0 | 1 |
3 | 4 | 4 | 0 | 1 |
4 | 6 | 6 | 0 | 1 |
5 | 6 | 6 | 0 | 1 |
6 | 6 | 6 | 0 | 1 |
7 | 4 | 4 | 0 | 1 |
8 | 2 | 2 | 0 | 1 |
9 | 1 | 1 | 0 | 1 |
10 | 1 | 1 | 0 | 1 |
e | #graphs | #cp | with mate | maxsz |
0 | 1 | 1 | 0 | 1 |
1 | 1 | 1 | 0 | 1 |
2 | 2 | 2 | 0 | 1 |
3 | 5 | 5 | 0 | 1 |
4 | 9 | 9 | 0 | 1 |
5 | 15 | 15 | 0 | 1 |
6 | 21 | 21 | 0 | 1 |
7 | 24 | 23 | 2 | 2 |
8 | 24 | 23 | 2 | 2 |
9 | 21 | 21 | 0 | 1 |
10 | 15 | 15 | 0 | 1 |
11 | 9 | 9 | 0 | 1 |
12 | 5 | 5 | 0 | 1 |
13 | 2 | 2 | 0 | 1 |
14 | 1 | 1 | 0 | 1 |
15 | 1 | 1 | 0 | 1 |
e | #graphs | #cp | with mate | maxsz |
0 | 1 | 1 | 0 | 1 |
1 | 1 | 1 | 0 | 1 |
2 | 2 | 2 | 0 | 1 |
3 | 5 | 5 | 0 | 1 |
4 | 10 | 10 | 0 | 1 |
5 | 21 | 21 | 0 | 1 |
6 | 41 | 38 | 5 | 3 |
7 | 65 | 60 | 10 | 2 |
8 | 97 | 88 | 18 | 2 |
9 | 131 | 121 | 20 | 2 |
10 | 148 | 141 | 12 | 3 |
11 | 148 | 141 | 12 | 3 |
12 | 131 | 121 | 20 | 2 |
13 | 97 | 88 | 18 | 2 |
14 | 65 | 60 | 10 | 2 |
15 | 41 | 38 | 5 | 3 |
16 | 21 | 21 | 0 | 1 |
17 | 10 | 10 | 0 | 1 |
18 | 5 | 5 | 0 | 1 |
19 | 2 | 2 | 0 | 1 |
20 | 1 | 1 | 0 | 1 |
21 | 1 | 1 | 0 | 1 |
e | #graphs | #cp | with mate | maxsz |
0 | 1 | 1 | 0 | 1 |
1 | 1 | 1 | 0 | 1 |
2 | 2 | 2 | 0 | 1 |
3 | 5 | 5 | 0 | 1 |
4 | 11 | 11 | 0 | 1 |
5 | 24 | 24 | 0 | 1 |
6 | 56 | 52 | 7 | 3 |
7 | 115 | 108 | 14 | 2 |
8 | 221 | 201 | 39 | 3 |
9 | 402 | 365 | 69 | 4 |
10 | 663 | 613 | 91 | 4 |
11 | 980 | 917 | 115 | 5 |
12 | 1312 | 1221 | 170 | 5 |
13 | 1557 | 1434 | 233 | 4 |
14 | 1646 | 1488 | 291 | 6 |
15 | 1557 | 1434 | 233 | 4 |
16 | 1312 | 1221 | 170 | 5 |
17 | 980 | 917 | 115 | 5 |
18 | 663 | 613 | 91 | 4 |
19 | 402 | 365 | 69 | 4 |
20 | 221 | 201 | 39 | 3 |
21 | 115 | 108 | 14 | 2 |
22 | 56 | 52 | 7 | 3 |
23 | 24 | 24 | 0 | 1 |
24 | 11 | 11 | 0 | 1 |
25 | 5 | 5 | 0 | 1 |
26 | 2 | 2 | 0 | 1 |
27 | 1 | 1 | 0 | 1 |
28 | 1 | 1 | 0 | 1 |
e | #graphs | #cp | with mate | maxsz |
0 | 1 | 1 | 0 | 1 |
1 | 1 | 1 | 0 | 1 |
2 | 2 | 2 | 0 | 1 |
3 | 5 | 5 | 0 | 1 |
4 | 11 | 11 | 0 | 1 |
5 | 25 | 25 | 0 | 1 |
6 | 63 | 59 | 7 | 3 |
7 | 148 | 138 | 19 | 3 |
8 | 345 | 314 | 60 | 3 |
9 | 771 | 688 | 156 | 4 |
10 | 1637 | 1470 | 306 | 4 |
11 | 3252 | 2962 | 535 | 5 |
12 | 5995 | 5482 | 954 | 6 |
13 | 10120 | 9235 | 1656 | 6 |
14 | 15615 | 14191 | 2642 | 9 |
15 | 21933 | 19995 | 3597 | 7 |
16 | 27987 | 25639 | 4373 | 6 |
17 | 32403 | 29901 | 4674 | 6 |
18 | 34040 | 31564 | 4637 | 6 |
19 | 32403 | 29901 | 4674 | 6 |
20 | 27987 | 25639 | 4373 | 6 |
21 | 21933 | 19995 | 3597 | 7 |
22 | 15615 | 14191 | 2642 | 9 |
23 | 10120 | 9235 | 1656 | 6 |
24 | 5995 | 5482 | 954 | 6 |
25 | 3252 | 2962 | 535 | 5 |
26 | 1637 | 1470 | 306 | 4 |
27 | 771 | 688 | 156 | 4 |
28 | 345 | 314 | 60 | 3 |
29 | 148 | 138 | 19 | 3 |
30 | 63 | 59 | 7 | 3 |
31 | 25 | 25 | 0 | 1 |
32 | 11 | 11 | 0 | 1 |
33 | 5 | 5 | 0 | 1 |
34 | 2 | 2 | 0 | 1 |
35 | 1 | 1 | 0 | 1 |
36 | 1 | 1 | 0 | 1 |
e | #graphs | #cp | with mate | maxsz |
1 | 1 | 1 | 0 | 1 |
2 | 2 | 2 | 0 | 1 |
3 | 5 | 5 | 0 | 1 |
4 | 11 | 11 | 0 | 1 |
5 | 26 | 26 | 0 | 1 |
6 | 66 | 62 | 7 | 3 |
7 | 165 | 154 | 21 | 3 |
8 | 428 | 389 | 75 | 3 |
9 | 1103 | 976 | 237 | 4 |
10 | 2769 | 2455 | 568 | 5 |
11 | 6759 | 6056 | 1279 | 5 |
12 | 15772 | 14304 | 2722 | 6 |
13 | 34663 | 31732 | 5455 | 7 |
14 | 71318 | 65735 | 10428 | 9 |
15 | 136433 | 126391 | 18826 | 10 |
16 | 241577 | 224880 | 31373 | 8 |
17 | 395166 | 369658 | 47972 | 11 |
18 | 596191 | 559706 | 68692 | 13 |
19 | 828728 | 779699 | 92350 | 12 |
20 | 1061159 | 997576 | 119163 | 15 |
21 | 1251389 | 1173357 | 145233 | 23 |
22 | 1358852 | 1271581 | 161818 | 19 |
23 | 1358852 | 1271581 | 161818 | 19 |
24 | 1251389 | 1173357 | 145233 | 23 |
25 | 1061159 | 997576 | 119163 | 15 |
26 | 828728 | 779699 | 92350 | 12 |
27 | 596191 | 559706 | 68692 | 13 |
28 | 395166 | 369658 | 47972 | 11 |
29 | 241577 | 224880 | 31373 | 8 |
30 | 136433 | 126391 | 18826 | 10 |
31 | 71318 | 65735 | 10428 | 9 |
32 | 34663 | 31732 | 5455 | 7 |
33 | 15772 | 14304 | 2722 | 6 |
34 | 6759 | 6056 | 1279 | 5 |
35 | 2769 | 2455 | 568 | 5 |
36 | 1103 | 976 | 237 | 4 |
37 | 428 | 389 | 75 | 3 |
38 | 165 | 154 | 21 | 3 |
39 | 66 | 62 | 7 | 3 |
40 | 26 | 26 | 0 | 1 |
41 | 11 | 11 | 0 | 1 |
42 | 5 | 5 | 0 | 1 |
43 | 2 | 2 | 0 | 1 |
44 | 1 | 1 | 0 | 1 |
45 | 1 | 1 | 0 | 1 |
e | #graphs | #cp | with mate | maxsz |
0 | 1 | 1 | 0 | 1 |
1 | 1 | 1 | 0 | 1 |
2 | 2 | 2 | 0 | 1 |
3 | 5 | 5 | 0 | 1 |
4 | 11 | 11 | 0 | 1 |
5 | 26 | 26 | 0 | 1 |
6 | 67 | 63 | 7 | 3 |
7 | 172 | 161 | 21 | 3 |
8 | 467 | 425 | 79 | 4 |
9 | 1305 | 1157 | 276 | 4 |
10 | 3664 | 3227 | 793 | 5 |
11 | 10250 | 9072 | 2128 | 6 |
12 | 28259 | 25251 | 5511 | 6 |
13 | 75415 | 68300 | 13095 | 7 |
14 | 192788 | 177042 | 29242 | 14 |
15 | 467807 | 434203 | 62858 | 15 |
16 | 1069890 | 1000573 | 130173 | 13 |
17 | 2295898 | 2159096 | 257453 | 13 |
18 | 4609179 | 4353188 | 483437 | 13 |
19 | 8640134 | 8186804 | 858901 | 12 |
20 | 15108047 | 14342950 | 1450889 | 16 |
21 | 24630887 | 23403071 | 2325548 | 28 |
22 | 37433760 | 35577973 | 3508525 | 21 |
23 | 53037356 | 50428733 | 4926016 | 21 |
24 | 70065437 | 66682056 | 6390926 | 29 |
25 | 86318670 | 82268821 | 7659772 | 33 |
26 | 99187806 | 94676147 | 8546114 | 31 |
27 | 106321628 | 101581920 | 8985654 | 32 |
28 | 106321628 | 101581920 | 8985654 | 32 |
29 | 99187806 | 94676147 | 8546114 | 31 |
30 | 86318670 | 82268821 | 7659772 | 33 |
31 | 70065437 | 66682056 | 6390926 | 29 |
32 | 53037356 | 50428733 | 4926016 | 21 |
33 | 37433760 | 35577973 | 3508525 | 21 |
34 | 24630887 | 23403071 | 2325548 | 28 |
35 | 15108047 | 14342950 | 1450889 | 16 |
36 | 8640134 | 8186804 | 858901 | 12 |
37 | 4609179 | 4353188 | 483437 | 13 |
38 | 2295898 | 2159096 | 257453 | 13 |
39 | 1069890 | 1000573 | 130173 | 13 |
40 | 467807 | 434203 | 62858 | 15 |
41 | 192788 | 177042 | 29242 | 14 |
42 | 75415 | 68300 | 13095 | 7 |
43 | 28259 | 25251 | 5511 | 6 |
44 | 10250 | 9072 | 2128 | 6 |
45 | 3664 | 3227 | 793 | 5 |
46 | 1305 | 1157 | 276 | 4 |
47 | 467 | 425 | 79 | 4 |
48 | 172 | 161 | 21 | 3 |
49 | 67 | 63 | 7 | 3 |
50 | 26 | 26 | 0 | 1 |
51 | 11 | 11 | 0 | 1 |
52 | 5 | 5 | 0 | 1 |
53 | 2 | 2 | 0 | 1 |
54 | 1 | 1 | 0 | 1 |
55 | 1 | 1 | 0 | 1 |
e | #graphs | #cp | with mate | maxsz |
0 | 1 | 1 | 0 | 1 |
1 | 1 | 1 | 0 | 1 |
2 | 2 | 2 | 0 | 1 |
3 | 5 | 5 | 0 | 1 |
4 | 11 | 11 | 0 | 1 |
5 | 26 | 26 | 0 | 1 |
6 | 68 | 64 | 7 | 3 |
7 | 175 | 164 | 21 | 3 |
8 | 485 | 442 | 81 | 4 |
9 | 1405 | 1247 | 295 | 4 |
10 | 4191 | 3684 | 914 | 5 |
11 | 12763 | 11218 | 2769 | 6 |
12 | 39243 | 34679 | 8262 | 7 |
13 | 119890 | 107348 | 22834 | 8 |
14 | 359307 | 326850 | 59682 | 14 |
15 | 1043774 | 963634 | 148946 | 15 |
16 | 2911086 | 2720244 | 357964 | 16 |
17 | 7739601 | 7300147 | 829099 | 18 |
18 | 19515361 | 18538338 | 1852312 | 16 |
19 | 46505609 | 44420144 | 3972194 | 24 |
20 | 104504341 | 100232767 | 8169019 | 23 |
21 | 221147351 | 212757285 | 16090529 | 28 |
22 | 440393606 | 424615658 | 30307025 | 30 |
23 | 825075506 | 796772409 | 54405586 | 27 |
24 | 1454265734 | 1406062027 | 92693467 | 31 |
25 | 2411961516 | 2334289130 | 149398201 | 47 |
26 | 3765262970 | 3646948156 | 227605271 | 45 |
27 | 5534255092 | 5363634223 | 328223775 | 58 |
28 | 7661345277 | 7427794910 | 449166015 | 67 |
29 | 9992340187 | 9688227140 | 584447282 | 84 |
30 | 12281841209 | 11905491932 | 722395037 | 92 |
31 | 14229503560 | 13788660723 | 844980527 | 108 |
32 | 15542350436 | 15056092725 | 930907383 | 138 |
33 | 16006173014 | 15503397759 | 962041146 | 226 |
34 | 15542350436 | 15056092725 | 930907383 | 138 |
35 | 14229503560 | 13788660723 | 844980527 | 108 |
36 | 12281841209 | 11905491932 | 722395037 | 92 |
37 | 9992340187 | 9688227140 | 584447282 | 84 |
38 | 7661345277 | 7427794910 | 449166015 | 67 |
39 | 5534255092 | 5363634223 | 328223775 | 58 |
40 | 3765262970 | 3646948156 | 227605271 | 45 |
41 | 2411961516 | 2334289130 | 149398201 | 47 |
42 | 1454265734 | 1406062027 | 92693467 | 31 |
43 | 825075506 | 796772409 | 54405586 | 27 |
44 | 440393606 | 424615658 | 30307025 | 30 |
45 | 221147351 | 212757285 | 16090529 | 28 |
46 | 104504341 | 100232767 | 8169019 | 23 |
47 | 46505609 | 44420144 | 3972194 | 24 |
48 | 19515361 | 18538338 | 1852312 | 16 |
49 | 7739601 | 7300147 | 829099 | 18 |
50 | 2911086 | 2720244 | 357964 | 16 |
51 | 1043774 | 963634 | 148946 | 15 |
52 | 359307 | 326850 | 59682 | 14 |
53 | 119890 | 107348 | 22834 | 8 |
54 | 39243 | 34679 | 8262 | 7 |
55 | 12763 | 11218 | 2769 | 6 |
56 | 4191 | 3684 | 914 | 5 |
57 | 1405 | 1247 | 295 | 4 |
58 | 485 | 442 | 81 | 4 |
59 | 175 | 164 | 21 | 3 |
60 | 68 | 64 | 7 | 3 |
61 | 26 | 26 | 0 | 1 |
62 | 11 | 11 | 0 | 1 |
63 | 5 | 5 | 0 | 1 |
64 | 2 | 2 | 0 | 1 |
65 | 1 | 1 | 0 | 1 |