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
| 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 |
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 |
| 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 |
| 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 |
| 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 |
| 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 |
| 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 |
| 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 |
| 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 |