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Four different views of Glasgow University Tower
Numbers of characteristic polynomials and cospectral graphs for A


n #graphs #char. pols #graphs with mate
0 1 1 0
1 1 1 0
2 2 2 0
3 4 4 0
4 11 11 0
5 34 33 2
6 156 151 10
7 1044 988 110
8 12346 11453 1722
9 274668 247357 51039
10 12005168 10608128 2560606
11 1018997864 901029366 215331676
12 165091172592 148187993520 31067572481

n=4 n=5 n=6 n=7 n=8 n=9 n=10 n=11 n=12

n=4


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

n=5


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 5 2 2
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

n=6


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 7 4 2
5 15 14 2 2
6 21 20 2 2
7 24 23 2 2
8 24 24 0 1
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

n=7


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 8 4 2
5 21 19 3 3
6 41 34 14 2
7 65 61 8 2
8 97 88 18 2
9 131 125 12 2
10 148 140 16 2
11 148 141 13 3
12 131 125 12 2
13 97 95 4 2
14 65 64 2 2
15 41 40 2 2
16 21 20 2 2
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

n=8


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 9 4 2
5 24 21 5 3
6 56 44 21 4
7 115 102 26 2
8 221 187 63 4
9 402 366 68 3
10 663 576 164 3
11 980 903 148 4
12 1312 1198 219 4
13 1557 1443 223 4
14 1646 1533 219 3
15 1557 1451 210 3
16 1312 1234 151 3
17 980 933 91 4
18 663 630 64 3
19 402 387 30 2
20 221 215 10 3
21 115 113 4 2
22 56 55 2 2
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

n=9


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 9 4 2
5 25 22 5 3
6 63 49 24 5
7 148 120 51 4
8 345 269 136 5
9 771 658 204 5
10 1637 1347 512 6
11 3252 2858 740 5
12 5995 5203 1419 6
13 10120 9012 2065 5
14 15615 13826 3282 7
15 21933 19637 4331 6
16 27987 24993 5513 10
17 32403 29064 6338 6
18 34040 30602 6404 6
19 32403 29261 5990 6
20 27987 25320 4931 10
21 21933 19988 3695 6
22 15615 14289 2458 6
23 10120 9331 1500 5
24 5995 5565 789 6
25 3252 3050 395 5
26 1637 1550 162 3
27 771 739 63 3
28 345 335 18 3
29 148 144 8 2
30 63 62 2 2
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

n=10


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 9 4 2
5 26 23 5 3
6 66 51 26 5
7 165 130 62 5
8 428 316 191 5
9 1103 873 412 5
10 2769 2144 1068 8
11 6759 5655 1994 7
12 15772 12992 4843 9
13 34663 29774 8874 9
14 71318 60763 18748 11
15 136433 118922 31852 12
16 241577 209938 56827 15
17 395166 346777 87986 12
18 596191 522518 133350 13
19 828728 729637 181236 14
20 1061159 933585 233250 21
21 1251389 1102637 273336 16
22 1358852 1198888 294399 15
23 1358852 1200673 291391 15
24 1251389 1106818 266294 16
25 1061159 940404 221659 21
26 828728 737004 168717 12
27 596191 531474 118267 13
28 395166 353751 76093 12
29 241577 217134 44628 15
30 136433 123348 24288 8
31 71318 64836 11928 8
32 34663 31776 5432 6
33 15772 14591 2188 5
34 6759 6322 840 5
35 2769 2615 290 4
36 1103 1054 94 3
37 428 414 26 3
38 165 162 6 2
39 66 65 2 2
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

n=11


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 9 4 1
5 26 23 5 1
6 67 52 26 5
7 172 135 65 5
8 467 336 220 6
9 1305 980 558 6
10 3664 2685 1617 9
11 10250 8181 3601 8
12 28259 22304 10088 10
13 75415 63021 21915 11
14 192788 160048 56851 16
15 467807 401830 118099 21
16 1069890 918366 269166 21
17 2295898 2001891 529579 16
18 4609179 4022395 1054698 21
19 8640134 7593806 1892068 20
20 15108047 13287522 3292566 31
21 24630887 21719491 5279190 30
22 37433760 33026554 8001477 39
23 53037356 46846429 11264629 35
24 70065437 61889850 14903754 36
25 86318670 76256313 18373280 31
26 99187806 87644859 21108349 46
27 106321628 93992968 22561018 34
28 106321628 94018562 22519077 34
29 99187806 87724533 20975573 46
30 86318670 76375210 18177143 31
31 70065437 62043591 14648996 36
32 53037356 47004809 11003951 34
33 37433760 33196606 7721507 33
34 24630887 21862432 5043664 30
35 15108047 13426080 3065242 30
36 8640134 7690246 1733808 20
37 4609179 4109009 913741 18
38 2295898 2052334 446687 16
39 1069890 959426 202832 15
40 467807 421573 85509 9
41 192788 174815 33221 9
42 75415 68958 12079 6
43 28259 26088 4048 5
44 10250 9582 1272 5
45 3664 3468 369 4
46 1305 1253 100 3
47 467 454 24 3
48 172 168 8 2
49 67 66 2 1
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

n=12


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 9 4 2
5 26 23 5 3
6 68 53 26 5
7 175 137 67 5
8 485 346 231 7
9 1405 1028 630 8
10 4191 2930 2038 10
11 12763 9621 5277 10
12 39243 29405 16193 14
13 119890 96137 40764 15
14 359307 287874 121006 21
15 1043774 876408 293842 24
16 2911086 2451075 802394 26
17 7739601 6685738 1878695 20
18 19515361 16911773 4633795 31
19 46505609 40829479 10226536 36
20 104504341 92009161 22529245 47
21 221147351 196003994 45623540 42
22 440393606 391210005 89333350 58
23 825075506 735607356 163077317 75
24 1454265734 1298678301 283881928 84
25 2411961516 2158074983 464168797 70
26 3765262970 3372225877 719283179 88
27 5534255092 4962042192 1048804378 77
28 7661345277 6873359123 1445744465 98
29 9992340187 8969183184 1879609773 87
30 12281841209 11026119614 2308811620 89
31 14229503560 12777398409 2672120188 106
32 15542350436 13959109693 2914822990 98
33 16006173014 14377992933 2998429426 128
34 15542350436 13960847673 2912011113 98
35 14229503560 12780531627 2667028735 106
36 12281841209 11030772434 2301299608 89
37 9992340187 8974361437 1871227811 92
38 7661345277 6879443698 1435979682 98
39 5534255092 4967640411 1039800439 77
40 3765262970 3378040813 710017278 88
41 2411961516 2162716257 456756771 88
42 1454265734 1303076951 276928481 84
43 825075506 738656475 158242526 75
44 440393606 393882268 85138580 52
45 221147351 197621776 43066062 42
46 104504341 93316379 20482028 37
47 46505609 41511313 9147293 26
48 19515361 17422116 3836007 23
49 7739601 6918134 1508450 17
50 2911086 2608210 557209 15
51 1043774 939397 192946 10
52 359307 325447 62764 10
53 119890 109562 19299 8
54 39243 36247 5598 6
55 12763 11945 1555 5
56 4191 3974 407 4
57 1405 1350 106 3
58 485 471 26 3
59 175 172 6 2
60 68 67 2 2
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
66 1 1 0 1