## Encodes the involutions E_2,...,E_7 defining G*. The involution E_i is given by involutions[i] (to make indexing less confusing, we set involutions[1] to be the list [1,...,4950]). ## Vertices are labeled by 1,2,...,4950 and involutions[i][x] = x if and only if vertex x does not admit an i-neighbor. involutions := [ [seq(j, j=1..4950)], [ 6, 13, 29, 4, 5, 1, 60, 8, 9, 10, 11, 50, 2, 30, 61, 46, 17, 18, 19, 44, 21, 36, 23, 24, 88, 125, 90, 77, 3, 14, 89, 32, 149, 34, 127, 22, 162, 38, 39, 112, 41, 98, 43, 20, 75, 16, 47, 69, 76, 12, 85, 52, 140, 54, 55, 56, 167, 141, 83, 7, 15, 72, 151, 64, 118, 66, 67, 215, 48, 204, 303, 62, 205, 278, 45, 49, 28, 78, 262, 224, 196, 82, 59, 84, 51, 285, 243, 25, 31, 27, 199, 92, 274, 94, 269, 96, 281, 42, 99, 218, 101, 102, 103, 251, 105, 253, 316, 308, 109, 110, 111, 40, 113, 114, 115, 264, 195, 65, 313, 263, 173, 122, 123, 124, 26, 209, 35, 237, 129, 326, 131, 132, 133, 134, 206, 136, 310, 240, 226, 53, 58, 275, 143, 144, 145, 332, 147, 299, 33, 150, 63, 258, 256, 154, 223, 156, 157, 158, 309, 233, 268, 37, 163, 290, 314, 166, 57, 181, 169, 170, 350, 567, 121, 552, 477, 176, 177, 347, 603, 180, 168, 182, 600, 475, 185, 427, 187, 188, 189, 190, 191, 490, 193, 194, 117, 81, 197, 198, 91, 513, 574, 202, 203, 70, 73, 135, 370, 208, 126, 515, 505, 212, 213, 358, 68, 361, 482, 100, 589, 517, 371, 443, 155, 80, 527, 139, 338, 429, 229, 230, 493, 232, 160, 533, 469, 373, 128, 238, 239, 138, 241, 598, 87, 503, 245, 246, 247, 248, 249, 250, 104, 440, 106, 392, 255, 153, 407, 152, 545, 458, 261, 79, 120, 116, 352, 266, 267, 161, 95, 270, 438, 414, 424, 93, 142, 355, 277, 74, 279, 587, 97, 282, 539, 501, 86, 461, 287, 288, 289, 164, 419, 292, 529, 294, 295, 296, 510, 558, 148, 300, 591, 302, 71, 586, 305, 456, 307, 108, 159, 137, 570, 441, 119, 165, 471, 107, 422, 532, 520, 496, 507, 353, 354, 452, 325, 130, 554, 328, 329, 330, 342, 146, 333, 578, 335, 336, 337, 227, 795, 340, 889, 331, 683, 344, 345, 962, 178, 348, 787, 171, 952, 265, 322, 323, 276, 747, 738, 214, 741, 360, 216, 362, 363, 364, 946, 675, 710, 368, 779, 207, 221, 985, 236, 374, 375, 918, 377, 378, 379, 380, 381, 382, 647, 384, 628, 386, 718, 388, 389, 390, 777, 254, 393, 394, 910, 396, 727, 703, 399, 987, 401, 402, 403, 680, 835, 406, 257, 966, 409, 410, 411, 636, 818, 272, 415, 416, 417, 904, 291, 420, 626, 317, 765, 273, 425, 854, 186, 428, 228, 816, 900, 961, 433, 631, 632, 436, 965, 271, 667, 252, 312, 896, 222, 444, 445, 783, 761, 448, 768, 964, 766, 324, 812, 454, 863, 306, 457, 260, 459, 656, 286, 799, 463, 464, 948, 892, 467, 841, 235, 470, 315, 472, 817, 474, 184, 611, 175, 950, 885, 691, 753, 217, 815, 916, 638, 486, 968, 488, 943, 192, 491, 492, 231, 494, 495, 320, 644, 498, 881, 500, 284, 619, 244, 504, 211, 506, 321, 935, 665, 297, 882, 512, 200, 514, 210, 959, 220, 742, 519, 319, 929, 822, 762, 524, 525, 526, 225, 724, 293, 657, 531, 318, 234, 534, 535, 536, 775, 928, 283, 540, 825, 542, 543, 878, 259, 546, 547, 873, 549, 744, 707, 174, 553, 327, 555, 556, 949, 298, 559, 695, 658, 748, 563, 564, 565, 610, 172, 704, 756, 311, 571, 669, 967, 201, 575, 576, 974, 334, 579, 938, 581, 991, 807, 584, 911, 304, 280, 588, 219, 840, 301, 856, 593, 640, 972, 755, 993, 242, 599, 183, 601, 754, 179, 1543, 605, 1388, 1316, 1206, 609, 566, 476, 1463, 1172, 614, 615, 1210, 1452, 618, 502, 620, 1051, 1352, 623, 624, 625, 421, 627, 385, 1228, 630, 434, 435, 1230, 1430, 1260, 412, 637, 485, 639, 594, 1237, 642, 643, 497, 645, 646, 383, 1166, 649, 650, 1116, 652, 1163, 654, 655, 460, 530, 561, 659, 660, 661, 662, 1263, 1406, 509, 1547, 439, 668, 572, 1190, 671, 672, 673, 674, 366, 1299, 677, 1252, 1342, 404, 1152, 682, 343, 684, 1136, 686, 687, 688, 689, 690, 480, 692, 693, 1086, 560, 1277, 1105, 698, 1225, 700, 1232, 702, 398, 568, 705, 1531, 551, 733, 709, 367, 711, 1367, 1205, 714, 715, 716, 1185, 387, 1092, 1434, 1402, 1268, 723, 528, 1094, 726, 397, 728, 729, 730, 1244, 732, 708, 734, 735, 736, 1161, 357, 1508, 1398, 359, 518, 1022, 550, 1506, 746, 356, 562, 1550, 750, 1518, 1449, 481, 602, 596, 569, 1099, 1461, 759, 1167, 447, 523, 763, 764, 423, 451, 1064, 449, 1250, 770, 1220, 772, 1024, 774, 537, 776, 391, 778, 369, 780, 781, 782, 446, 1245, 1330, 1087, 349, 1349, 1312, 790, 1410, 792, 793, 794, 339, 1279, 797, 1328, 462, 1440, 1469, 1035, 1235, 1292, 1436, 806, 583, 808, 809, 1309, 811, 453, 1067, 814, 483, 430, 473, 413, 1076, 1108, 821, 522, 823, 824, 541, 826, 1340, 1379, 1418, 830, 1411, 832, 833, 834, 405, 1246, 837, 1154, 839, 590, 468, 842, 843, 1373, 1479, 846, 1381, 1218, 849, 850, 851, 1530, 1331, 426, 1044, 592, 1238, 858, 859, 1542, 861, 1017, 455, 864, 865, 866, 1335, 1055, 1438, 1113, 871, 1160, 548, 874, 1048, 1310, 1171, 544, 879, 880, 499, 511, 883, 1476, 479, 886, 1072, 1196, 341, 890, 1546, 466, 1201, 1254, 895, 442, 1075, 898, 1031, 431, 1204, 902, 1109, 418, 1389, 1157, 907, 908, 909, 395, 585, 912, 1480, 1541, 915, 484, 917, 376, 1527, 920, 921, 1540, 923, 1069, 925, 926, 927, 538, 521, 930, 931, 1004, 1248, 1285, 508, 936, 1003, 580, 1175, 1054, 1303, 942, 489, 944, 1256, 365, 947, 465, 557, 478, 1503, 351, 1437, 1178, 955, 956, 957, 958, 516, 960, 432, 346, 963, 450, 437, 408, 573, 487, 1091, 1500, 1126, 595, 1070, 577, 975, 976, 1482, 978, 1118, 1281, 981, 982, 1356, 984, 372, 1453, 400, 988, 1383, 1539, 582, 1520, 597, 1124, 995, 996, 1360, 998, 2224, 1829, 1001, 2042, 937, 932, 1005, 1891, 1007, 1008, 2150, 1717, 1725, 1991, 1013, 1759, 1746, 1016, 862, 2066, 2078, 1631, 1815, 743, 1023, 773, 1565, 1892, 1027, 1028, 1029, 1030, 899, 2033, 1043, 1502, 802, 1036, 1037, 1038, 1841, 1888, 1890, 1587, 1033, 855, 1045, 2055, 1047, 875, 1262, 1050, 621, 1852, 2232, 940, 868, 1738, 1663, 1058, 1570, 1060, 1817, 1062, 1063, 767, 2091, 1066, 813, 2127, 924, 973, 1071, 887, 1613, 1074, 897, 819, 1077, 2046, 2170, 1080, 1081, 1442, 1083, 1781, 1320, 694, 786, 1088, 1089, 1090, 969, 719, 1093, 725, 1095, 1096, 1097, 1098, 757, 1824, 2098, 1102, 1103, 1104, 697, 1889, 1107, 820, 903, 2074, 1977, 1444, 870, 1114, 1880, 651, 1117, 979, 1119, 1120, 1121, 1122, 1123, 994, 1125, 971, 2056, 1219, 1129, 1130, 1575, 1132, 2187, 1134, 1135, 685, 1697, 1138, 2075, 1798, 1141, 1142, 2051, 1144, 1832, 2243, 1658, 1148, 1149, 2200, 1151, 681, 1368, 838, 1155, 1156, 906, 1158, 1159, 872, 737, 1162, 653, 1164, 1165, 648, 760, 1168, 1199, 1681, 877, 613, 1173, 1597, 939, 1787, 1177, 954, 1801, 2032, 1181, 1581, 1993, 1970, 717, 1186, 2198, 1188, 1189, 670, 1858, 1823, 1193, 1194, 2021, 888, 1197, 1917, 1169, 1596, 893, 1952, 2181, 901, 713, 608, 1624, 2049, 1906, 616, 1825, 1212, 1843, 1836, 1215, 1790, 2162, 848, 1128, 771, 1599, 1915, 1978, 1224, 699, 1226, 1700, 629, 1729, 633, 1231, 701, 1962, 1655, 803, 2214, 641, 857, 1989, 2112, 2020, 1242, 2088, 731, 784, 836, 1247, 933, 1249, 769, 2175, 678, 1253, 894, 1255, 945, 1922, 1614, 1259, 635, 1608, 1049, 663, 2128, 1265, 1266, 2048, 722, 1269, 1270, 1271, 2095, 1273, 1676, 1275, 1276, 696, 2171, 796, 1908, 980, 1282, 1283, 1284, 934, 1286, 1287, 1288, 1951, 1290, 1964, 804, 2143, 1294, 1959, 1296, 1297, 1621, 676, 1300, 2222, 1709, 941, 2227, 1305, 1907, 1985, 1711, 810, 876, 1607, 789, 1313, 1913, 1315, 607, 1371, 2237, 1319, 1085, 1321, 1867, 1323, 1324, 1325, 2076, 1814, 798, 1329, 785, 853, 1332, 1635, 1334, 867, 1916, 2082, 1338, 1339, 827, 2093, 679, 1879, 1344, 1345, 1346, 1347, 1348, 788, 1679, 1351, 622, 2225, 1354, 1355, 983, 1357, 1909, 1359, 997, 1361, 1362, 1363, 1364, 1665, 1366, 712, 1153, 2239, 1370, 1317, 2154, 844, 1374, 2018, 1491, 1377, 1378, 828, 1380, 847, 1382, 989, 1384, 1615, 1386, 1387, 606, 905, 1955, 1695, 1997, 1662, 1811, 1395, 2036, 1397, 740, 1399, 1400, 1401, 721, 1403, 1404, 1840, 664, 1834, 1408, 1617, 791, 831, 1412, 1413, 1414, 1415, 1647, 2037, 829, 1419, 1420, 1421, 1422, 1423, 1696, 2052, 1426, 1926, 1428, 1429, 634, 1431, 2177, 1630, 720, 1928, 805, 953, 869, 1439, 800, 1971, 1082, 1443, 1112, 1445, 1446, 1874, 1448, 752, 1910, 1451, 617, 986, 1454, 1455, 1456, 1457, 2083, 2166, 1976, 758, 1462, 612, 2146, 1465, 1466, 2235, 1468, 801, 1470, 1576, 1472, 1473, 2099, 1475, 884, 1674, 1627, 845, 913, 1481, 977, 1483, 1682, 2000, 1981, 1487, 1855, 1489, 1490, 1376, 2054, 1493, 1494, 1495, 1958, 2138, 2015, 1900, 970, 1501, 1034, 951, 2001, 1505, 745, 1507, 739, 1509, 1510, 1593, 1512, 1553, 2134, 1873, 1585, 1774, 751, 1519, 992, 2167, 1522, 2183, 2217, 2124, 1526, 919, 1528, 2204, 852, 706, 1532, 1533, 2209, 1598, 2133, 1537, 1606, 990, 922, 914, 860, 604, 1544, 1545, 891, 666, 1548, 2122, 749, 1551, 1552, 1513, 2009, 1972, 1643, 1557, 2629, 1580, 2499, 1719, 1562, 2079, 1564, 1025, 1945, 1567, 2265, 2311, 1059, 2588, 2208, 1573, 1574, 1131, 1471, 1577, 2626, 2560, 1559, 1182, 1582, 1583, 1882, 1516, 1765, 1042, 1588, 1589, 2004, 1591, 2510, 1511, 1594, 1822, 1200, 1174, 1535, 1221, 1600, 2665, 1602, 1771, 2142, 2137, 1538, 1311, 1261, 1609, 1633, 2647, 1707, 1073, 1258, 1385, 2275, 1409, 2617, 1794, 2169, 1298, 2388, 1623, 1207, 2555, 2027, 1478, 1677, 1629, 1433, 1020, 2131, 1610, 2593, 1333, 1636, 1637, 1638, 1639, 2490, 1641, 2468, 1556, 1644, 1645, 2474, 1416, 1648, 1649, 1650, 2532, 1652, 1653, 1654, 1234, 2386, 1657, 1147, 1659, 1660, 2190, 1393, 1057, 1819, 1365, 2576, 1667, 1668, 1669, 2654, 1838, 2472, 1673, 1477, 1675, 1274, 1628, 1678, 1350, 2425, 1170, 1484, 1876, 1684, 1919, 1686, 1687, 2485, 2299, 1690, 2596, 2542, 1693, 2203, 1391, 1424, 1137, 2294, 1699, 1227, 2545, 1702, 1703, 2383, 2302, 1706, 1612, 1708, 1302, 1710, 1308, 1712, 2570, 1714, 1715, 1716, 1010, 2556, 1561, 2420, 1721, 1722, 1723, 1724, 1011, 1726, 1727, 1728, 1229, 2614, 2296, 2271, 1733, 2256, 1735, 1846, 1737, 1056, 2199, 2395, 2482, 1742, 1743, 1744, 2550, 1015, 2262, 1768, 1749, 1750, 1986, 1752, 2147, 1754, 1755, 2251, 2249, 1758, 1014, 2610, 2666, 2276, 1763, 2259, 1586, 2449, 2416, 1748, 1769, 1770, 1603, 1772, 2139, 1517, 1775, 1776, 1777, 1778, 2374, 1780, 1084, 1782, 2084, 1784, 2319, 2252, 1176, 1788, 1789, 1216, 2362, 1792, 1793, 1619, 1861, 2274, 2213, 1140, 2361, 2400, 1179, 2584, 1803, 1804, 1805, 2014, 1807, 1808, 1854, 2669, 1394, 2353, 1813, 1327, 1021, 1816, 1061, 2323, 1664, 2057, 1821, 1595, 1192, 1100, 1211, 1826, 1828, 1827, 1000, 2365, 1831, 1145, 2031, 1407, 1835, 1214, 2008, 1671, 2341, 1405, 1039, 1842, 1213, 1896, 1845, 1736, 1847, 2298, 1849, 1850, 2470, 1052, 2402, 1809, 1488, 2178, 2248, 1191, 1859, 1860, 1795, 1862, 2461, 1864, 1865, 2058, 1322, 1868, 2646, 1870, 1871, 2405, 1515, 1447, 1875, 1683, 1877, 1878, 1343, 1115, 2475, 1584, 2418, 2291, 2434, 1886, 1887, 1040, 1106, 1041, 1006, 1026, 1960, 2534, 1895, 1844, 1897, 1898, 1899, 1499, 2349, 2140, 1903, 1904, 2667, 1209, 1306, 1280, 1358, 1450, 1911, 1912, 1314, 1914, 1222, 1336, 1198, 1918, 1685, 2663, 2279, 1257, 1923, 1924, 1925, 1427, 1927, 1435, 1929, 2639, 1931, 2537, 1933, 2289, 1935, 1936, 2254, 1938, 1967, 1940, 1941, 1942, 1943, 2064, 1566, 1946, 1957, 1948, 2135, 1950, 1289, 1202, 1953, 2263, 1390, 2192, 1947, 1496, 1295, 1893, 2520, 1233, 1963, 1291, 1965, 2565, 1939, 1968, 2438, 1184, 1441, 1555, 2641, 2157, 1975, 1460, 1111, 1223, 1979, 1980, 1486, 1982, 1983, 2318, 1307, 1751, 2606, 2363, 1239, 2450, 1012, 1992, 1183, 1994, 1995, 2660, 1392, 1998, 1999, 1485, 1504, 2002, 2003, 1590, 2280, 2006, 2007, 1837, 1554, 2010, 2011, 2526, 2444, 1806, 1498, 2306, 2017, 1375, 2019, 1241, 1195, 2022, 2600, 2442, 2025, 2564, 1626, 2028, 2029, 2546, 1833, 1180, 1032, 2034, 2035, 1396, 1417, 2038, 2668, 2356, 2397, 1002, 2043, 2530, 2045, 1078, 2047, 1267, 1208, 2050, 1143, 1425, 2549, 1492, 1046, 1127, 1820, 1866, 2059, 2060, 2061, 2062, 2063, 1944, 2065, 1018, 2067, 2630, 2069, 2070, 2071, 2072, 2465, 1110, 1139, 1326, 2424, 1019, 1563, 2080, 2081, 1337, 1458, 1783, 2379, 2086, 2087, 1243, 2089, 2206, 1065, 2552, 1341, 2174, 1272, 2096, 2486, 1101, 1474, 2100, 2572, 2102, 2419, 2451, 2352, 2106, 2443, 2108, 2623, 2359, 2111, 1240, 2553, 2172, 2115, 2396, 2218, 2118, 2119, 2120, 2121, 1549, 2523, 1525, 2125, 2126, 1068, 1264, 2129, 2130, 1632, 2132, 1536, 1514, 1949, 2136, 1605, 1497, 1773, 1902, 2531, 1604, 1293, 2144, 2411, 1464, 1753, 2346, 2149, 1009, 2151, 2197, 2334, 1372, 2155, 2156, 1974, 2158, 2624, 2317, 2540, 1217, 2163, 2164, 2393, 1459, 1521, 2168, 1620, 1079, 1278, 2114, 2173, 2094, 1251, 2371, 1432, 1856, 2179, 2504, 1203, 2182, 1523, 2350, 2185, 2406, 1133, 2188, 2189, 1661, 2191, 1956, 2193, 2194, 2521, 2196, 2152, 1187, 1739, 1150, 2201, 2202, 1694, 1529, 2205, 2090, 2324, 1572, 1534, 2210, 2607, 2467, 1797, 1236, 2215, 2216, 1524, 2117, 2662, 2220, 2221, 1301, 2454, 999, 1353, 2601, 1304, 2228, 2229, 2230, 2231, 1053, 2267, 2234, 1467, 2345, 1318, 2320, 1369, 2240, 2544, 2242, 1146, 2244, 2575, 2246, 3321, 1857, 1757, 2250, 1756, 1786, 3316, 1937, 2255, 1734, 2257, 3388, 1764, 2942, 2261, 1747, 1954, 3301, 1568, 2266, 2233, 2268, 3235, 2377, 1732, 2702, 2273, 1796, 1616, 1762, 3236, 2278, 1921, 2005, 2824, 3226, 2283, 2284, 2285, 2978, 2287, 2288, 1934, 2732, 1884, 2292, 2293, 1698, 2295, 1731, 2972, 1848, 1689, 2300, 3283, 1705, 3159, 2304, 2863, 2016, 2307, 3132, 2476, 2310, 1569, 2312, 2763, 2314, 3292, 2466, 2160, 1984, 1785, 2238, 2321, 2496, 1818, 2207, 2886, 2936, 2768, 3062, 2398, 2330, 2834, 2332, 2333, 2153, 2335, 2336, 2337, 2338, 2339, 2340, 1839, 2342, 2343, 2950, 2236, 2148, 3041, 2796, 1901, 2184, 2351, 2105, 1812, 2701, 2366, 2040, 2357, 2358, 2110, 2360, 1799, 1791, 1988, 3179, 1830, 2355, 2367, 2368, 2799, 2842, 2176, 2372, 3308, 1779, 2885, 3150, 2270, 2578, 2085, 2921, 2381, 2382, 1704, 2441, 2896, 1656, 2387, 1622, 2389, 3076, 2391, 2392, 2165, 2394, 1740, 2116, 2041, 2329, 2399, 1800, 2401, 1853, 2403, 2525, 1872, 2186, 3197, 2423, 2595, 2410, 2145, 2412, 2649, 2811, 2415, 1767, 2417, 1883, 2103, 1720, 2421, 2690, 2408, 2077, 1680, 2426, 2427, 3230, 2429, 3353, 2431, 2432, 2839, 1885, 2435, 2436, 2437, 1969, 2439, 2680, 2384, 2024, 2107, 2013, 2865, 2789, 2447, 2655, 1766, 1990, 2104, 2452, 2698, 2223, 2455, 2456, 2833, 2458, 2892, 2460, 1863, 2462, 2463, 2803, 2073, 2316, 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2161, 1808, 3301, 2070, 2788, 2513, 2966, 2515, 2920, 3289, 2518, 2011, 2405, 1978, 2864, 2523, 2524, 2767, 2526, 1968, 1591, 2615, 2530, 2531, 2001, 1735, 1614, 2652, 2433, 2055, 3367, 3139, 2965, 2168, 2542, 1863, 2037, 1570, 2546, 2547, 2548, 2200, 2183, 2551, 1972, 1829, 2554, 2555, 2556, 2223, 2604, 2559, 2646, 2561, 2562, 2100, 2564, 2663, 2129, 2932, 2711, 2569, 2570, 1589, 2051, 2173, 2574, 2575, 2786, 2577, 3280, 1611, 2071, 1653, 3086, 3180, 2584, 2234, 2586, 1849, 3353, 2202, 2590, 2918, 3306, 2593, 3110, 1719, 2596, 2184, 2598, 2599, 3350, 2763, 1839, 2196, 2558, 2605, 2789, 2406, 2962, 2609, 3236, 2901, 2612, 2613, 2863, 2529, 2616, 2345, 1770, 3238, 2879, 2089, 2845, 1928, 2449, 3262, 1908, 2040, 2628, 2629, 2630, 3390, 2632, 2633, 3360, 3216, 1779, 2637, 3191, 2000, 2640, 1880, 2642, 3251, 2644, 3229, 2560, 2827, 2648, 2031, 2650, 2651, 2535, 2023, 2654, 2655, 2712, 2657, 2658, 2659, 2803, 2661, 2662, 2565, 2664, 1624, 2082, 2265, 1781, 2093, 1992, 2160, 2672, 2693, 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