Norton-Smith Graph

Author

Eric W. Weisstein
March 4, 2021

This notebook downloaded from http://mathworld.wolfram.com/notebooks/GraphTheory/Norton-SmithGraph.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/Norton-SmithGraph.html.

©2021 Wolfram Research, Inc. except for portions noted otherwise

Source

https://www.distanceregular.org/graphs/norton-smith.html

https://www.distanceregular.org/graphdata/norton-smith.g

Construction

GAP

## Antipodal 3-cover of SRG(378,117,36,36) from O_7(3) (cf. BCN, page 400)
## 1134 vertices, diameter 4, aut. gp. 3.O_7(3):2, i.e. 3.PGO(7,3)
## Generators from wwwATLAS
## Graph constructed implicitly by Norton 1988

gap> LoadPackage("grape");;

gap> nortonsmith:=EdgeOrbitsGraph( Group(
  [ (   2,   3)(   4,   6)(   5,   8)(   9,  13)(  10,  15)(  11,  17)(  12,  19)(  14,  22)(  16,  25)(  18,  28)
    (  20,  31)(  21,  33)(  23,  36)(  24,  38)(  26,  41)(  27,  43)(  29,  46)(  30,  47)(  32,  50)(  34,  53)
    (  35,  48)(  37,  56)(  39,  59)(  40,  61)(  42,  64)(  44,  67)(  49,  73)(  51,  76)(  52,  78)(  54,  81)
    (  55,  83)(  57,  86)(  58,  87)(  60,  90)(  62,  92)(  63,  94)(  65,  96)(  66,  98)(  68, 101)(  69, 103)
    (  70, 105)(  71, 107)(  74, 111)(  75, 113)(  77, 116)(  79, 119)(  80, 121)(  82, 124)(  84, 120)(  85, 128)
    (  88, 132)(  89, 134)(  91, 137)(  93, 140)(  95, 143)(  97, 146)(  99, 148)( 100, 150)( 102, 153)( 104, 156)
    ( 106, 159)( 108, 162)( 109, 164)( 110, 166)( 112, 169)( 114, 172)( 115, 174)( 117, 177)( 118, 178)( 122, 183)
    ( 125, 187)( 126, 189)( 127, 191)( 129, 193)( 131, 196)( 135, 200)( 136, 202)( 138, 205)( 139, 207)( 141, 210)
    ( 142, 212)( 144, 215)( 145, 217)( 147, 220)( 149, 223)( 151, 226)( 152, 228)( 154, 231)( 155, 232)( 157, 234)
    ( 158, 236)( 160, 239)( 161, 241)( 163, 213)( 165, 238)( 168, 249)( 173, 255)( 175, 258)( 176, 260)( 180, 264)
    ( 181, 259)( 182, 267)( 184, 270)( 185, 272)( 186, 274)( 188, 277)( 190, 279)( 192, 281)( 194, 263)( 195, 285)
    ( 197, 288)( 198, 290)( 199, 292)( 201, 294)( 203, 297)( 209, 302)( 211, 305)( 214, 309)( 216, 312)( 218, 315)
    ( 219, 262)( 221, 319)( 222, 321)( 224, 324)( 225, 326)( 227, 329)( 229, 332)( 233, 337)( 235, 340)( 237, 342)
    ( 240, 346)( 242, 349)( 243, 351)( 244, 353)( 245, 273)( 246, 356)( 247, 357)( 248, 251)( 250, 358)( 252, 266)
    ( 253, 362)( 254, 364)( 256, 366)( 257, 368)( 261, 373)( 265, 377)( 268, 380)( 269, 336)( 271, 350)( 275, 386)
    ( 276, 388)( 278, 391)( 280, 394)( 282, 383)( 284, 398)( 286, 401)( 287, 403)( 289, 406)( 291, 408)( 293, 410)
    ( 295, 413)( 296, 415)( 298, 418)( 299, 420)( 300, 422)( 301, 424)( 303, 427)( 304, 429)( 306, 432)( 307, 433)
    ( 308, 435)( 310, 437)( 311, 439)( 313, 441)( 314, 443)( 316, 446)( 317, 448)( 318, 450)( 320, 452)( 323, 456)
    ( 325, 459)( 328, 462)( 330, 461)( 331, 425)( 333, 468)( 334, 470)( 335, 472)( 339, 395)( 341, 478)( 343, 480)
    ( 344, 482)( 345, 484)( 347, 487)( 352, 493)( 354, 494)( 359, 479)( 360, 499)( 361, 500)( 363, 502)( 365, 504)
    ( 367, 379)( 369, 507)( 370, 509)( 372, 512)( 374, 515)( 375, 517)( 378, 521)( 381, 524)( 382, 525)( 385, 529)
    ( 387, 530)( 389, 445)( 390, 498)( 392, 535)( 393, 537)( 396, 490)( 397, 542)( 399, 545)( 402, 531)( 404, 549)
    ( 405, 551)( 407, 554)( 409, 555)( 411, 558)( 414, 438)( 416, 564)( 417, 565)( 419, 568)( 421, 571)( 423, 444)
    ( 428, 575)( 430, 580)( 431, 582)( 440, 590)( 442, 589)( 447, 581)( 449, 593)( 451, 598)( 453, 601)( 454, 603)
    ( 455, 605)( 457, 608)( 458, 609)( 460, 611)( 463, 614)( 465, 485)( 466, 618)( 471, 540)( 473, 624)( 474, 511)
    ( 475, 626)( 476, 628)( 477, 629)( 481, 633)( 483, 636)( 486, 637)( 489, 641)( 491, 560)( 495, 647)( 496, 649)
    ( 497, 650)( 503, 654)( 505, 539)( 506, 527)( 508, 658)( 510, 660)( 513, 664)( 514, 666)( 516, 546)( 519, 670)
    ( 520, 671)( 522, 673)( 526, 676)( 528, 679)( 532, 682)( 533, 683)( 534, 588)( 538, 688)( 541, 691)( 543, 616)
    ( 544, 573)( 547, 696)( 548, 698)( 552, 703)( 553, 702)( 556, 648)( 557, 707)( 559, 643)( 561, 652)( 562, 712)
    ( 563, 713)( 566, 714)( 567, 716)( 569, 717)( 574, 721)( 577, 669)( 578, 620)( 579, 727)( 583, 594)( 584, 731)
    ( 585, 640)( 586, 645)( 591, 739)( 592, 740)( 595, 675)( 596, 744)( 597, 677)( 599, 606)( 600, 747)( 602, 681)
    ( 604, 752)( 610, 751)( 613, 760)( 615, 689)( 617, 765)( 619, 725)( 621, 769)( 622, 771)( 623, 772)( 625, 775)
    ( 627, 684)( 630, 742)( 632, 782)( 634, 781)( 635, 786)( 638, 693)( 639, 788)( 642, 791)( 644, 793)( 646, 795)
    ( 651, 708)( 653, 797)( 656, 694)( 657, 800)( 659, 802)( 662, 806)( 665, 809)( 672, 815)( 674, 718)( 678, 821)
    ( 680, 705)( 685, 825)( 690, 830)( 695, 787)( 697, 837)( 699, 746)( 700, 839)( 704, 817)( 709, 842)( 710, 738)
    ( 711, 822)( 715, 846)( 719, 720)( 722, 849)( 724, 847)( 729, 852)( 730, 757)( 732, 764)( 733, 856)( 734, 794)
    ( 735, 859)( 737, 774)( 741, 743)( 748, 869)( 749, 870)( 750, 872)( 753, 835)( 754, 851)( 755, 875)( 756, 841)
    ( 758, 878)( 759, 816)( 761, 882)( 762, 803)( 763, 880)( 766, 888)( 767, 838)( 768, 850)( 770, 891)( 776, 860)
    ( 777, 780)( 778, 834)( 779, 873)( 783, 901)( 789, 865)( 796, 799)( 798, 911)( 801, 814)( 804, 826)( 807, 920)
    ( 808, 922)( 810, 921)( 811, 926)( 812, 820)( 813, 927)( 818, 931)( 819, 932)( 824, 833)( 827, 936)( 828, 915)
    ( 829, 939)( 831, 940)( 836, 945)( 840, 950)( 843, 908)( 845, 952)( 848, 955)( 854, 886)( 855, 958)( 861, 961)
    ( 863, 963)( 866, 962)( 867, 883)( 868, 966)( 871, 968)( 876, 956)( 877, 946)( 879, 914)( 881, 971)( 885, 974)
    ( 887, 969)( 890, 980)( 892, 982)( 893, 983)( 894, 985)( 897, 988)( 898, 990)( 900, 903)( 902, 994)( 904, 997)
    ( 905, 941)( 906, 996)( 907, 999)( 909, 919)( 910,1001)( 912,1003)( 913,1004)( 916,1006)( 917, 935)( 918, 944)
    ( 924, 943)( 925,1011)( 929,1014)( 933,1016)( 934, 964)( 937,1005)( 938,1019)( 942, 992)( 947, 970)( 948,1025)
    ( 949,1026)( 951,1028)( 954,1015)( 957, 979)( 959, 977)( 960,1032)( 967,1017)( 973,1037)( 975,1041)( 978,1021)
    ( 981,1045)( 987,1008)( 991,1000)( 993,1030)( 995,1054)( 998,1057)(1007,1065)(1009,1068)(1010,1070)(1012,1073)
    (1013,1064)(1018,1039)(1020,1077)(1023,1079)(1024,1058)(1027,1042)(1033,1084)(1034,1083)(1035,1038)(1036,1047)
    (1043,1086)(1044,1088)(1048,1080)(1049,1092)(1050,1093)(1052,1095)(1059,1100)(1060,1090)(1061,1096)(1066,1104)
    (1067,1105)(1069,1108)(1071,1094)(1072,1107)(1074,1110)(1076,1085)(1081,1091)(1087,1111)(1089,1118)(1098,1122)
    (1099,1123)(1101,1114)(1109,1124)(1115,1117)(1120,1129)(1125,1132)(1126,1128)(1133,1134), 
  (   1,   2,   4,   7,  11,  18,  29)(   3,   5,   9,  14,  23,  37,  57)(   6,  10,  16,  26,  42,  65,  97)
    (   8,  12,  20,  32,  51,  77, 117)(  13,  21,  34,  54,  82, 125, 188)(  15,  24,  39,  60,  91, 138, 206)
    (  17,  27,  44,  68, 102, 154, 132)(  19,  30,  48,  72, 109, 165, 246)(  22,  35,  55,  84, 127, 192, 282)
    (  25,  40,  62,  93, 141, 211, 306)(  28,  45,  69, 104, 157, 235, 341)(  31,  49,  74, 112, 170, 252, 312)
    (  33,  52,  79, 120, 181, 266, 379)(  36,  43,  66,  99, 149, 224, 325)(  38,  58,  88, 133, 198, 291, 319)
    (  41,  63,  95, 144, 216, 313, 442)(  46,  70, 106, 160, 240, 347, 488)(  47,  71, 108, 163, 244, 354, 496)
    (  50,  75, 114, 173, 256, 367, 506)(  53,  80, 122, 184, 271, 384, 528)(  56,  85, 129, 194, 284, 399, 478)
    (  59,  89, 135, 201, 295, 414, 562)(  61,  92, 139, 208, 231, 335, 473)(  64,  96, 145, 218, 316, 447, 596)
    (  67, 100, 151, 227, 330, 465, 617)(  73, 110, 167, 248, 281, 396, 541)(  76, 115, 175, 259, 371, 511, 662)
    (  78, 118, 179, 263, 356, 498, 652)(  81, 123, 185, 273, 385, 517, 626)(  83, 126, 190, 177, 262, 375, 518)
    (  86, 130, 195, 286, 402, 547, 697)(  87, 131, 197, 289, 407, 448, 200)(  90, 136, 203, 298, 419, 569, 718)
    (  94, 142, 213, 308, 436, 587, 735)(  98, 147, 221, 320, 453, 602, 750)( 101, 152, 229, 333, 469, 172, 254)
    ( 103, 155, 233, 338, 475, 627, 777)( 105, 158, 237, 343, 481, 634, 785)( 107, 161, 242, 350, 491, 644, 459)
    ( 111, 168, 250, 360, 234, 339, 476)( 113, 171, 253, 363, 503, 655, 799)( 116, 176, 261, 374, 516, 669, 813)
    ( 119, 180, 265, 378, 522, 636, 787)( 121, 182, 268, 381, 429, 579, 683)( 124, 186, 275, 387, 531, 681, 823)
    ( 128, 159, 238, 344, 483, 629, 779)( 134, 199, 293, 411, 559, 709, 843)( 137, 204, 299, 421, 572, 422, 573)
    ( 140, 209, 303, 428, 578, 726, 401)( 143, 214, 310, 438, 589, 737, 861)( 146, 219, 317, 449, 597, 745, 867)
    ( 148, 222, 322, 455, 606, 754, 499)( 150, 225, 327, 461, 487, 640, 267)( 153, 230, 334, 471, 549, 700, 568)
    ( 156, 220, 318, 451, 599, 746, 868)( 162, 243, 352, 494, 558, 708, 841)( 164, 245, 355, 497, 651, 752, 178)
    ( 166, 247, 358, 255, 365, 505, 656)( 169, 251, 361, 437, 588, 736, 860)( 174, 257, 369, 508, 659, 803, 916)
    ( 183, 269, 382, 526, 677, 820, 933)( 187, 276, 389, 533, 684, 824, 934)( 189, 278, 392, 536, 686, 826, 935)
    ( 191, 280, 395, 540, 690, 831, 670)( 193, 283, 397, 543, 693, 833, 942)( 196, 287, 404, 550, 701, 493, 646)
    ( 202, 296, 416, 535, 685, 394, 539)( 205, 300, 423, 292, 409, 556, 706)( 207, 301, 425, 575, 723, 850, 530)
    ( 210, 304, 430, 581, 728, 853, 926)( 212, 307, 434, 585, 733, 857, 960)( 215, 311, 440, 591, 679, 822, 290)
    ( 217, 314, 444, 593, 601, 749, 871)( 223, 323, 457, 609, 756, 876, 309)( 226, 328, 463, 615, 763, 885, 975)
    ( 228, 331, 466, 619, 767, 889, 979)( 232, 336, 450, 403, 548, 699, 782)( 236, 342, 479, 631, 781, 900, 992)
    ( 239, 345, 485, 638, 789, 906, 272)( 241, 348, 489, 642, 555, 582, 729)( 249, 359, 362, 501, 653, 798, 912)
    ( 258, 370, 510, 661, 805, 918, 391)( 260, 372, 513, 665, 810, 925,1012)( 264, 376, 519, 509, 660, 804, 917)
    ( 270, 383, 527, 678, 698, 838, 948)( 274, 373, 514, 667, 812, 837, 947)( 277, 390, 534, 605, 415, 563, 521)
    ( 279, 393, 538, 689, 829, 564, 368)( 285, 400, 546, 618, 766, 713, 845)( 288, 405, 552, 704, 840, 932,1015)
    ( 294, 412, 560, 710, 793, 875, 712)( 297, 417, 566, 715, 847, 954, 598)( 302, 426, 576, 724, 580, 676, 747)
    ( 305, 431, 583, 730, 854, 957, 717)( 315, 445, 594, 742, 865, 964,1035)( 321, 454, 604, 753, 874, 825, 500)
    ( 324, 458, 610, 757, 877, 366, 439)( 326, 460, 612, 759, 880, 418, 567)( 329, 464, 616, 764, 886, 976,1042)
    ( 332, 467, 620, 768, 666, 811, 869)( 337, 474, 625, 776, 897, 989,1025)( 340, 477, 630, 780, 899, 502, 504)
    ( 346, 486, 639, 790, 907,1000,1060)( 349, 490, 643, 792, 744, 866, 965)( 351, 492, 645, 794, 859, 962,1034)
    ( 353, 495, 648, 796, 909, 565, 714)( 357, 480, 632, 783, 902, 995,1055)( 364, 380, 523, 427, 577, 725, 851)
    ( 377, 520, 672, 816, 929, 940,1022)( 386, 515, 668, 468, 621, 770, 892)( 388, 532, 624, 774, 895, 986,1047)
    ( 398, 544, 694, 834, 943,1024,1081)( 406, 553, 682, 791, 908, 931, 997)( 408, 525, 675, 819, 727, 852, 956)
    ( 410, 557, 590, 738, 739, 862, 842)( 413, 561, 711, 844, 951, 846, 953)( 420, 570, 719, 703, 786, 904, 983)
    ( 424, 574, 722, 795, 472, 623, 773)( 432, 452, 600, 748, 721, 849, 647)( 433, 584, 732, 855, 959,1031,1083)
    ( 435, 586, 734, 858, 961,1033,1028)( 441, 592, 741, 864, 950, 963, 649)( 443, 545, 695, 835, 944, 507, 657)
    ( 446, 595, 743, 470, 622, 551, 702)( 456, 607, 608, 755, 740, 863, 707)( 462, 613, 761, 883, 973, 802, 915)
    ( 482, 635, 775, 896, 987,1048,1091)( 484, 637, 788, 905, 998,1058,1099)( 512, 663, 807, 921,1007,1066, 982)
    ( 524, 674, 818, 806, 919, 974,1040)( 529, 680, 628, 778, 898, 991,1051)( 537, 687, 827, 937,1018,1076,1073)
    ( 542, 692, 832, 941,1023,1080,1115)( 554, 705, 771, 893, 984, 571, 720)( 603, 751, 873, 970,1038,1004,1062)
    ( 611, 758, 879, 968,1037, 815, 928)( 614, 762, 884, 839, 949,1027,1019)( 633, 784, 903, 996,1056,1097,1092)
    ( 641, 772, 894, 696, 836, 946, 654)( 650, 691, 821, 830, 891, 800, 913)( 658, 801, 914,1005,1063,1102,1104)
    ( 664, 808, 923,1009,1069, 952,1029)( 671, 814, 882, 972,1039,1085,1108)( 673, 817, 930, 985, 870, 967,1036)
    ( 688, 828, 938,1020, 936,1017,1075)( 716, 848, 939,1021,1078,1113,1126)( 731, 765, 887, 977,1032,1084,1116)
    ( 760, 881, 945, 958,1030,1001,1061)( 769, 890, 981,1046,1090,1120,1130)( 797, 910,1002, 878, 971,1016, 856)
    ( 809, 924,1010,1071,1109,1125,1095)( 872, 969, 994,1053,1096,1077,1112)( 888, 978,1043,1087,1117,1127,1133)
    ( 901, 993,1052,1003, 988,1049, 966)( 911, 922,1008,1067,1106,1124,1132)( 920, 990,1050,1094,1121,1131,1054)
    ( 927,1013,1074,1111,1123,1129,1134)( 955,1014, 980,1044,1089,1119,1041)( 999,1059,1101,1093,1011,1072,1045)
    (1006,1064,1088,1118,1128,1026,1082)(1057,1098,1122,1070,1065,1103,1086)(1068,1107,1110,1079,1114,1100,1105) ] ),
	[1,7] );

rec( isGraph := true, order := 1134, group := <permutation group with 2 generators>, schreierVector := [ -1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 
      1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 
      2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 1, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 
      1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 2, 
      2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 2, 2, 2, 1, 
      2, 1, 2, 1, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 
      2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 
      1, 2, 2, 1, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 2, 2, 2, 2, 1, 1, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 
      2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 1, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 
      1, 2, 2, 1, 1, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 
      2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 
      1, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 
      2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 1, 2, 2, 2, 1, 1, 2, 2, 2, 1, 2, 2, 1, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 1, 
      2, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 2, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 
      2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 1, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2 ], 
  adjacencies := [ [ 7, 11, 17, 24, 38, 54, 60, 81, 90, 115, 123, 155, 167, 171, 174, 182, 204, 206, 208, 232, 240, 245, 267, 273, 287, 295, 296, 304, 346, 352, 355, 361, 367, 375, 379, 384, 400, 403, 413, 415, 426, 429, 430, 434, 458, 469, 
          493, 500, 503, 517, 522, 541, 547, 570, 572, 580, 604, 607, 609, 612, 625, 654, 655, 668, 673, 686, 691, 692, 696, 726, 732, 737, 752, 764, 774, 775, 784, 792, 811, 832, 844, 853, 863, 866, 879, 884, 892, 894, 898, 914, 926, 928, 930, 
          938, 962, 963, 976, 982, 985, 990, 1009, 1019, 1022, 1029, 1036, 1047, 1048, 1055, 1063, 1066, 1068, 1080, 1097, 1104, 1115, 1117, 1121 ] ], representatives := [ 1 ], isSimple := true )

gap> IsDistanceRegular(nortonsmith);
true

gap> UndirectedEdges(nortonsmith);

edgeliststring=;

ReadGAPEdgeList[f_String]:=ToExpression[StringReplace[f,{"["->"{","]"->"}"}]]

Length[e=ReadGAPEdgeList[edgeliststring]]

g=Graph[Union[Flatten[e]],UndirectedEdge@@@e]

RecognizeGraph[g]

Properties

VertexCount[g]

GraphDiameter[g]

RegularParameters[g]

IntersectionArray[g]//Timing

<<IGraphM`

IGIntersectionArray[g]

IntegerSpectrum[g]//SpectrumForm

DistanceRegularGraphQ[g]//Timing

DistanceTransitiveGraphQ[g]//Timing

GraphData

GraphDataClassString

GraphDataClassString[g]

GraphDataString

file=OpenAppend["~/dr.m"]

WriteString[file,GraphDataString[g,
"StandardName"->"NortonSmithGraph",
"Name"->"Norton\[Hyphen]Smith graph",
"Information"->"Norton-SmithGraph",
"Embeddings"->{},
"Skip"->{"Arboricity","BurningNumber","Chord","ChordlessCycle","ChordlessCycles","Chords","ChromaticNumber","CliqueCoveringNumber","ComplementOddChordlessCycle","ComplementOddChordlessCycles","ConnectedInducedSubgraphPolynomial","ConnectedInducedSubgraphs","CrossingNumber","Cycles","CyclePolynomial","DominatingSet","DominatingSets","EdgeCovers","GracefulLabeling","GracefulLabelings","HamiltonianCycles","HamiltonianPaths","HamiltonianWalks","IdiosyncraticPolynomial","IndependentVertexSets","LongestCycles","MatchingGeneratingPolynomial","MaximalIndependentEdgeSets","MaximalIndependentVertexSets","MaximallyNonhamiltonian","MaximumFlowMatrix","MaximumIndependentEdgeSets","MinimumCoveringsByMaximalCliques","MinimumEdgeColoring","MinimumVertexColoring","MinimumVertexCut","MinimumVertexCuts","MinimumWeightFractionalColoring","MinimumWeightFractionalEdgeColoring","OddChordlessCycles","PathPolynomial","Paths","RadioLabeling","RadioLabelings","RadioNumber","RectilinearCrossingCount","ResistanceMatrix","Skewness","StronglyPerfect","UnitDistance","Thickness"},
TimeConstraint->10
]]

Close[file]