Constructions of isospectral circulant graphs

How to Distinguish Cospectral Graphs

“…Two non-isomorphic graphs having an identical spectrum are said to be cospectral (or isospectral); we shall use the same word as well for the adjacency matrices associated with these graphs. For an enumeration of such pairs of cospectral graphs, we refer to [4] and for a construction to [5].…”

“…, 19, 16, 13, 10, −∞, 0} Its generalized characteristic polynomial is (−144p 2 − 852p 3 − 1894p 4 − 566p 5 + 9198p6 + 36, 082p7 + 89, 232p8 + 175, 664p9 + 294, 184p10 + 421, 560p11 + 508, 064p12 + 505, 344p13 + 407, 488p14 + 260, 160p15 + 126, 592p16 + 44, 032p 17 + 9728p 18 + 1024p19 ) + (−96p − 584p 2 − 1320p 3 + 23p 4 + 10, 606p5 + 43, 979p6 + 115, 528p7 + 233, 112p8 + 388, 704p9 + 552, 060p10 + 674, 112p11 + 708, 416p12 + 639, 040p13 + 492, 000p14 + 319, 680p15 + 171, 520p16 + 73, 088p 17 + 23, 168p 18 + 4864p 19 + 512p 20 )λ + (−16 − 148p − 276p 2 + 764p 3 + 6364p 4 + 23, 516p 5 + 60, 856p 6 + 122, 864p 7 + 204, 440p 8 + 287, 392p 9 + 345, 856p 10 + 360, 912p 11 + 329, 824p 12 + 264, 320p 13 + 183, 872p 14 + 108, 288p 15 + 51, 584p 16 + 18, 432p 17 + 4352p 18 + 512p 19 )λ 2 + (−16 + 24p + 438p 2 + 2084p 3 + 6965p 4 + 17, 208p 5 + 33, 348p 6 + 53, 592p 7 + 72, 840p 8 + 84, 800p 9 + 85, 344p 10 + 73, 920p 11 + 54, 144p 12 + 32, 320p 13 + 14, 592p 14 + 4352p 15 + 640p 16 )λ 3 + (10 + 98p + 390p 2 + 1162p 3 + 2616p 4 + 4728p 5 + 7200p 6 + 9144p 7 + 9696p 8 + 8592p 9 + 6240p 10 + 3520p 11 + 1344p 12 + 256p 13 )λ 4 + (11 + 30p + 89p 2 + 192p 3 + 300p 4 + 392p 5 + 412p 6 + 352p 7 + 256p 8 + 128p 9 + 32p 10 )λ 5 2, 834, 095, 486, 447, 385, 236, 929, 913, 169, 689, 691, 637, 492, 733, 459, 538, 837, 652, 638, 768, 165, 548, 958, 207, 737, 274, 222, 940, 398, 813, 184p 174 + 3, 715, 162, 412, 897, 587, 037, 462, 302, 535, 386, 744, 023, 914, 256, 120, 989, 946, 829, 375, 400, 222, 661, 205, 895, 799, 449, 710, 438, 196, 969, 472p 175 + 4, 767, 959, 628, 941, 108, 000, 797, 613, 858, 464, 148, 917, 669, 255, 071, 446, 598, 694, 244, 111, 728, 677, 437, 055, 573, 610, 319, 036, 660, 318, 208p 176 + 5, 987, 677, 874, 629, 381, 685, 999, 335, 024, 243, 924, 219, 129, 977, 623, 753, 150, 341, 364, 591, 794, 295, 205, 378, 872, 432, 492, 389, 129, 519, 104p 177 + 7, 353, 981, 344, 895, 744, 352, 463, 648, 571, 230, 490, 792, 300, 355, 595, 347, 964, 422, 028, 926, 020, 781, 326, 875, 135, 262, 952, 943, 121, 334, 272p 178 + 8, 828, 322, 363, 162, 102, 502, 750, 728, 620, 669, 579, 320, 036, 651, 534, 660, 710, 241, 255, 782, 587, 192, 505, 508, 851, 854, 854, 448, 341, 843, 968p 179 + 10, 352, 932, 581, 109, 219, 242, 714, 479, 624, 563, 234, 784, 776, 021, 623, 751, 678, 087, 591, 648, 503, 683, 557, 166, 712, 645, 262, 134, 353, 068, 032p 180 + 11, 852, 199, 893, 356, 307, 877, 507...…”

Cospectral constructions and spectral properties of variations of the distance matrix

“…Mönius [44] used results from number theory to show when two circulant graphs were cospectral with respect to the adjacency matrix.…”