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 | 10 | 2 | 2 |
5 | 34 | 32 | 4 | 2 |
6 | 156 | 148 | 16 | 2 |
7 | 1044 | 992 | 102 | 3 |
8 | 12346 | 11718 | 1201 | 4 |
9 | 274668 | 264807 | 19001 | 5 |
10 | 12005168 | 11674848 | 636607 | 9 |
11 | 1018997864 | 999003763 | 38966931 | 20 |
12 | 165091172592 | 162807642839 | 4476641637 | 42 |
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 |
1 | 1 | 1 | 0 | 1 |
2 | 2 | 2 | 0 | 1 |
3 | 3 | 2 | 2 | 2 |
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 | 3 | 2 | 2 |
4 | 6 | 6 | 0 | 1 |
5 | 6 | 6 | 0 | 1 |
6 | 6 | 6 | 0 | 1 |
7 | 4 | 3 | 2 | 2 |
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 | 4 | 2 | 2 |
4 | 9 | 8 | 2 | 2 |
5 | 15 | 15 | 0 | 1 |
6 | 21 | 21 | 0 | 1 |
7 | 24 | 22 | 4 | 2 |
8 | 24 | 22 | 4 | 2 |
9 | 21 | 21 | 0 | 1 |
10 | 15 | 15 | 0 | 1 |
11 | 9 | 8 | 2 | 2 |
12 | 5 | 4 | 2 | 2 |
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 | 10 | 8 | 4 | 2 |
4 | 10 | 9 | 2 | 2 |
5 | 21 | 20 | 2 | 2 |
6 | 41 | 40 | 2 | 2 |
7 | 65 | 62 | 6 | 2 |
8 | 97 | 91 | 12 | 2 |
9 | 131 | 124 | 14 | 2 |
10 | 148 | 142 | 11 | 2 |
11 | 148 | 142 | 11 | 3 |
12 | 131 | 124 | 14 | 2 |
13 | 97 | 91 | 12 | 2 |
14 | 65 | 62 | 6 | 2 |
15 | 41 | 40 | 2 | 2 |
16 | 21 | 20 | 2 | 2 |
17 | 10 | 9 | 2 | 2 |
18 | 5 | 4 | 2 | 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 | 10 | 8 | 4 | 2 |
4 | 11 | 10 | 2 | 2 |
5 | 24 | 22 | 4 | 2 |
6 | 56 | 52 | 7 | 2 |
7 | 115 | 107 | 16 | 2 |
8 | 221 | 203 | 36 | 2 |
9 | 402 | 372 | 58 | 3 |
10 | 663 | 621 | 79 | 3 |
11 | 980 | 932 | 93 | 3 |
12 | 1312 | 1260 | 100 | 4 |
13 | 1557 | 1482 | 142 | 4 |
14 | 1646 | 1558 | 167 | 4 |
15 | 1557 | 1482 | 141 | 4 |
16 | 1312 | 1261 | 98 | 4 |
17 | 980 | 935 | 86 | 4 |
18 | 663 | 628 | 66 | 3 |
19 | 402 | 376 | 51 | 3 |
20 | 221 | 208 | 26 | 2 |
21 | 115 | 108 | 14 | 2 |
22 | 56 | 53 | 5 | 3 |
23 | 24 | 22 | 4 | 2 |
24 | 11 | 10 | 2 | 2 |
25 | 5 | 4 | 2 | 2 |
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 | 4 | 2 | 2 |
4 | 11 | 10 | 2 | 2 |
5 | 25 | 23 | 4 | 2 |
6 | 63 | 58 | 9 | 3 |
7 | 148 | 136 | 24 | 2 |
8 | 345 | 320 | 50 | 2 |
9 | 771 | 723 | 93 | 3 |
10 | 1637 | 1540 | 179 | 5 |
11 | 3252 | 3099 | 293 | 4 |
12 | 5995 | 5769 | 433 | 4 |
13 | 10120 | 9762 | 688 | 4 |
14 | 15615 | 15043 | 1109 | 4 |
15 | 21933 | 21093 | 1635 | 4 |
16 | 27987 | 26978 | 1958 | 5 |
17 | 32403 | 31312 | 2086 | 4 |
18 | 34040 | 32946 | 2071 | 4 |
19 | 32403 | 31319 | 2075 | 4 |
20 | 27987 | 26989 | 1940 | 5 |
21 | 21933 | 21103 | 1619 | 4 |
22 | 15615 | 15058 | 1081 | 4 |
23 | 10120 | 9779 | 656 | 4 |
24 | 5995 | 5783 | 408 | 4 |
25 | 3252 | 3107 | 278 | 4 |
26 | 1637 | 1558 | 149 | 4 |
27 | 771 | 728 | 84 | 3 |
28 | 345 | 326 | 38 | 2 |
29 | 148 | 137 | 22 | 2 |
30 | 63 | 59 | 7 | 3 |
31 | 25 | 23 | 4 | 2 |
32 | 11 | 10 | 2 | 2 |
33 | 5 | 4 | 2 | 2 |
34 | 2 | 2 | 0 | 1 |
35 | 1 | 1 | 0 | 1 |
36 | 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 | 4 | 2 | 2 |
4 | 11 | 10 | 2 | 2 |
5 | 26 | 24 | 4 | 2 |
6 | 66 | 60 | 11 | 3 |
7 | 165 | 149 | 31 | 2 |
8 | 428 | 388 | 80 | 2 |
9 | 1103 | 1022 | 155 | 4 |
10 | 2769 | 2587 | 338 | 6 |
11 | 6759 | 6399 | 681 | 4 |
12 | 15772 | 15090 | 1307 | 4 |
13 | 34663 | 33445 | 2344 | 5 |
14 | 71318 | 69067 | 4362 | 4 |
15 | 136433 | 132293 | 8069 | 5 |
16 | 241577 | 234458 | 13909 | 7 |
17 | 395166 | 383937 | 21814 | 5 |
18 | 596191 | 579866 | 31495 | 6 |
19 | 828728 | 806636 | 42534 | 7 |
20 | 1061159 | 1032890 | 54427 | 9 |
21 | 1251389 | 1217370 | 65430 | 9 |
22 | 1358852 | 1321256 | 72165 | 9 |
23 | 1358852 | 1321255 | 72181 | 9 |
24 | 1251389 | 1217418 | 65338 | 9 |
25 | 1061159 | 1032965 | 54290 | 9 |
26 | 828728 | 806738 | 42342 | 7 |
27 | 596191 | 579961 | 31312 | 6 |
28 | 395166 | 384023 | 21660 | 5 |
29 | 241577 | 234561 | 13716 | 5 |
30 | 136433 | 132379 | 7919 | 5 |
31 | 71318 | 69153 | 4202 | 4 |
32 | 34663 | 33510 | 2224 | 5 |
33 | 15772 | 15157 | 1182 | 4 |
34 | 6759 | 6450 | 590 | 4 |
35 | 2769 | 2633 | 259 | 4 |
36 | 1103 | 1038 | 128 | 3 |
37 | 428 | 398 | 60 | 2 |
38 | 165 | 151 | 27 | 3 |
39 | 66 | 61 | 9 | 3 |
40 | 26 | 24 | 4 | 2 |
41 | 11 | 10 | 2 | 2 |
42 | 5 | 4 | 2 | 2 |
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 | 4 | 2 | 2 |
4 | 11 | 10 | 2 | 2 |
5 | 26 | 24 | 4 | 2 |
6 | 67 | 61 | 11 | 2 |
7 | 172 | 155 | 33 | 3 |
8 | 467 | 420 | 93 | 3 |
9 | 1305 | 1198 | 205 | 4 |
10 | 3664 | 3405 | 487 | 6 |
11 | 10250 | 9671 | 1092 | 5 |
12 | 28259 | 26924 | 2536 | 4 |
13 | 75415 | 72567 | 5436 | 6 |
14 | 192788 | 186703 | 11713 | 6 |
15 | 467807 | 454829 | 25201 | 6 |
16 | 1069890 | 1042608 | 53338 | 10 |
17 | 2295898 | 2240997 | 107427 | 7 |
18 | 4609179 | 4505188 | 203086 | 8 |
19 | 8640134 | 8455252 | 360278 | 10 |
20 | 15108047 | 14798366 | 602866 | 11 |
21 | 24630887 | 24139559 | 956313 | 12 |
22 | 37433760 | 36695764 | 1436639 | 16 |
23 | 53037356 | 51993405 | 2033387 | 12 |
24 | 70065437 | 68687523 | 2686072 | 12 |
25 | 86318670 | 84631681 | 3290167 | 13 |
26 | 99187806 | 97269707 | 3739927 | 20 |
27 | 106321628 | 104282252 | 3973874 | 20 |
28 | 106321628 | 104282351 | 3973697 | 20 |
29 | 99187806 | 97269919 | 3739550 | 20 |
30 | 86318670 | 84632027 | 3289553* | 13 |
31 | 70065437 | 68687924 | 2685316 | 12 |
32 | 53037356 | 51993928 | 2032407 | 12 |
33 | 37433760 | 36696381 | 1435463 | 16 |
34 | 24630887 | 24140330 | 954838 | 12 |
35 | 15108047 | 14799173 | 601329 | 9 |
36 | 8640134 | 8456061 | 358747 | 10 |
37 | 4609179 | 4505871 | 201801 | 8 |
38 | 2295898 | 2241532 | 106447 | 7 |
39 | 1069890 | 1043007 | 52593 | 10 |
40 | 467807 | 455109 | 24695 | 6 |
41 | 192788 | 186936 | 11291 | 6 |
42 | 75415 | 72727 | 5152 | 6 |
43 | 28259 | 27074 | 2261 | 4 |
44 | 10250 | 9759 | 936 | 4 |
45 | 3664 | 3467 | 378 | 4 |
46 | 1305 | 1217 | 173 | 3 |
47 | 467 | 431 | 71 | 2 |
48 | 172 | 157 | 29 | 3 |
49 | 67 | 62 | 9 | 3 |
50 | 26 | 24 | 4 | 2 |
51 | 11 | 10 | 2 | 2 |
52 | 5 | 5 | 0 | 1 |
53 | 2 | 2 | 0 | 1 |
54 | 1 | 1 | 0 | 1 |
55 | 1 | 1 | 0 | 1 |
The * indicates a correction to the figure of 3289555 that was given in the paper by Haemers and Spence.
e | #graphs | #cp | with mate | maxsz |
0 | 1 | 1 | 0 | 1 |
1 | 1 | 1 | 0 | 1 |
2 | 2 | 2 | 0 | 1 |
3 | 5 | 4 | 2 | 2 |
4 | 11 | 10 | 2 | 2 |
5 | 26 | 24 | 4 | 2 |
6 | 68 | 62 | 11 | 3 |
7 | 175 | 157 | 35 | 3 |
8 | 485 | 434 | 100 | 3 |
9 | 1405 | 1276 | 246 | 4 |
10 | 4191 | 3854 | 630 | 6 |
11 | 12763 | 11934 | 1547 | 7 |
12 | 39243 | 37066 | 4094 | 6 |
13 | 119890 | 114618 | 9991 | 8 |
14 | 359307 | 346329 | 24811 | 6 |
15 | 1043774 | 1012573 | 60189 | 8 |
16 | 2911086 | 2836427 | 145203 | 10 |
17 | 7739601 | 7564465 | 342501 | 8 |
18 | 19515361 | 19117238 | 780313 | 8 |
19 | 46505609 | 45636700 | 1703279 | 10 |
20 | 104504341 | 102693370 | 3548703 | 11 |
21 | 221147351 | 217548897 | 7051462 | 12 |
22 | 440393606 | 433580546 | 13355795 | 16 |
23 | 825075506 | 812775813 | 24125153 | 22 |
24 | 1454265734 | 1433132369 | 41477954 | 22 |
25 | 2411961516 | 2377512373 | 67645822 | 20 |
26 | 3765262970 | 3712180245 | 104255411 | 20 |
27 | 5534255092 | 5457060270 | 151584296 | 20 |
28 | 7661345277 | 7555397762 | 207956531 | 24 |
29 | 9992340187 | 9854950806 | 269523097 | 40 |
30 | 12281841209 | 12113414975 | 330197523 | 36 |
31 | 14229503560 | 14034414540 | 382205312 | 36 |
32 | 15542350436 | 15329117432 | 417514154 | 41 |
33 | 16006173014 | 15786494843 | 430036552 | 42 |
34 | 15542350436 | 15329126504 | 417497214 | 41 |
35 | 14229503560 | 14034428220 | 382179425 | 36 |
36 | 12281841209 | 12113434248 | 330160980 | 36 |
37 | 9992340187 | 9854975519 | 269476213 | 40 |
38 | 7661345277 | 7555427319 | 207900721 | 24 |
39 | 5534255092 | 5457086052 | 151535437 | 20 |
40 | 3765262970 | 3712201659 | 104214784 | 20 |
41 | 2411961516 | 2377528881 | 67614383 | 20 |
42 | 1454265734 | 1433146706 | 41450407 | 22 |
43 | 825075506 | 812786998 | 24103521 | 22 |
44 | 440393606 | 433590429 | 13336634 | 16 |
45 | 221147351 | 217557006 | 7035791 | 12 |
46 | 104504341 | 102699904 | 3536170 | 9 |
47 | 46505609 | 45640913 | 1695271 | 10 |
48 | 19515361 | 19120093 | 774972 | 8 |
49 | 7739601 | 7566265 | 339177 | 8 |
50 | 2911086 | 2837794 | 142695 | 10 |
51 | 1043774 | 1013403 | 58709 | 8 |
52 | 359307 | 347034 | 23545 | 6 |
53 | 119890 | 115034 | 9269 | 6 |
54 | 39243 | 37415 | 3477 | 6 |
55 | 12763 | 12082 | 1300 | 4 |
56 | 4191 | 3935 | 490 | 4 |
57 | 1405 | 1300 | 205 | 4 |
58 | 485 | 446 | 76 | 3 |
59 | 175 | 159 | 31 | 3 |
60 | 68 | 63 | 9 | 3 |
61 | 26 | 24 | 4 | 2 |
62 | 11 | 10 | 2 | 2 |
63 | 5 | 4 | 2 | 2 |
64 | 2 | 2 | 0 | 1 |
65 | 1 | 1 | 0 | 1 |
66 | 1 | 1 | 0 | 1 |