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On this page are computer-accessible forms for the graph C4[ 108, 21 ] = UG(ATD[108,30]).

(I) Following is a form readable by MAGMA:

g:=Graph<108|{ {66, 67}, {12, 14}, {72, 74}, {10, 14}, {1, 4}, {27, 30}, {51, 54}, {1, 7}, {90, 92}, {27, 29}, {51, 53}, {66, 68}, {3, 4}, {90, 93}, {1, 9}, {2, 10}, {4, 13}, {86, 95}, {82, 91}, {19, 26}, {1, 10}, {36, 47}, {6, 13}, {101, 105}, {34, 47}, {101, 104}, {64, 77}, {71, 74}, {82, 92}, {16, 31}, {21, 26}, {66, 77}, {7, 22}, {5, 22}, {13, 25}, {65, 85}, {7, 18}, {42, 63}, {39, 50}, {9, 28}, {64, 85}, {5, 19}, {15, 25}, {75, 93}, {4, 19}, {42, 61}, {37, 50}, {9, 30}, {7, 16}, {74, 93}, {72, 80}, {72, 81}, {5, 24}, {8, 22}, {8, 40}, {28, 60}, {14, 46}, {66, 98}, {9, 40}, {17, 48}, {15, 46}, {11, 42}, {18, 48}, {69, 103}, {11, 40}, {65, 98}, {18, 55}, {79, 106}, {28, 58}, {30, 56}, {23, 48}, {10, 34}, {25, 49}, {13, 37}, {2, 43}, {30, 55}, {20, 61}, {11, 34}, {27, 49}, {28, 54}, {14, 37}, {29, 54}, {18, 57}, {31, 51}, {69, 104}, {19, 61}, {31, 49}, {2, 45}, {16, 33}, {27, 41}, {26, 41}, {83, 103}, {3, 54}, {89, 108}, {15, 57}, {90, 108}, {86, 96}, {3, 52}, {15, 56}, {23, 47}, {88, 96}, {89, 96}, {17, 43}, {83, 105}, {80, 106}, {16, 43}, {87, 108}, {87, 107}, {92, 97}, {87, 105}, {86, 105}, {92, 99}, {8, 73}, {8, 75}, {36, 103}, {24, 91}, {2, 70}, {35, 103}, {3, 70}, {39, 98}, {24, 93}, {39, 97}, {5, 76}, {6, 76}, {44, 102}, {45, 102}, {17, 94}, {6, 84}, {20, 70}, {6, 82}, {22, 64}, {31, 73}, {53, 99}, {23, 64}, {53, 98}, {59, 99}, {26, 67}, {60, 101}, {61, 100}, {25, 67}, {60, 102}, {62, 100}, {20, 72}, {56, 100}, {56, 101}, {60, 99}, {52, 84}, {44, 77}, {46, 79}, {52, 85}, {53, 84}, {44, 78}, {32, 67}, {52, 87}, {35, 71}, {32, 69}, {35, 70}, {62, 88}, {63, 88}, {12, 100}, {41, 65}, {32, 73}, {40, 65}, {11, 97}, {38, 76}, {12, 102}, {46, 68}, {57, 83}, {38, 77}, {47, 68}, {57, 82}, {58, 81}, {50, 94}, {12, 97}, {55, 90}, {32, 78}, {33, 78}, {49, 94}, {55, 88}, {59, 75}, {62, 78}, {17, 96}, {29, 108}, {58, 75}, {33, 83}, {62, 76}, {24, 107}, {51, 71}, {33, 84}, {42, 95}, {37, 80}, {50, 71}, {58, 79}, {63, 74}, {38, 80}, {41, 95}, {63, 73}, {29, 106}, {35, 91}, {45, 85}, {34, 91}, {36, 94}, {43, 81}, {36, 95}, {45, 86}, {20, 104}, {23, 107}, {21, 104}, {44, 81}, {21, 107}, {39, 89}, {59, 69}, {21, 106}, {38, 89}, {48, 79}, {59, 68} }>;

(II) A more general form is to represent the graph as the orbit of {66, 67} under the group generated by the following permutations:

a: (2, 22, 3, 40)(4, 9, 10, 7)(5, 54, 11, 43)(6, 27, 12, 48)(8, 70)(13, 30, 14, 18)(16, 19, 28, 34)(17, 76, 29, 97)(20, 75, 35, 73)(21, 99, 36, 78)(23, 84, 41, 102)(24, 51, 42, 81)(25, 56, 46, 57)(26, 60, 47, 33)(31, 61, 58, 91)(32, 104, 59, 103)(37, 55)(38, 108, 39, 96)(44, 107, 53, 95)(45, 64, 52, 65)(49, 100, 79, 82)(50, 88, 80, 90)(62, 106, 92, 94)(63, 72, 93, 71)(66, 105)(67, 101, 68, 83)(77, 87, 98, 86)
b: (1, 2, 3)(4, 10, 70)(5, 12, 71)(6, 11, 72)(7, 45, 54)(8, 44, 53)(9, 43, 52)(13, 34, 20)(14, 35, 19)(15, 36, 21)(16, 85, 28)(17, 87, 30)(18, 86, 29)(22, 102, 51)(23, 101, 49)(24, 100, 50)(25, 47, 104)(26, 46, 103)(27, 48, 105)(31, 64, 60)(32, 66, 59)(33, 65, 58)(37, 91, 61)(38, 92, 63)(39, 93, 62)(40, 81, 84)(41, 79, 83)(42, 80, 82)(55, 96, 108)(56, 94, 107)(57, 95, 106)(67, 68, 69)(73, 77, 99)(74, 76, 97)(75, 78, 98)(88, 89, 90)
c: (2, 3)(4, 10)(5, 11)(6, 12)(7, 9)(13, 14)(16, 28)(17, 29)(18, 30)(19, 34)(20, 35)(21, 36)(22, 40)(23, 41)(24, 42)(25, 46)(26, 47)(27, 48)(31, 58)(32, 59)(33, 60)(38, 39)(43, 54)(44, 53)(45, 52)(49, 79)(50, 80)(51, 81)(56, 57)(61, 91)(62, 92)(63, 93)(64, 65)(67, 68)(71, 72)(73, 75)(76, 97)(77, 98)(78, 99)(82, 100)(83, 101)(84, 102)(86, 87)(88, 90)(94, 106)(95, 107)(96, 108)(103, 104)
d: (1, 4, 13, 25, 49, 31, 16, 7)(2, 5, 14, 26, 50, 32, 17, 8)(3, 6, 15, 27, 51, 33, 18, 9)(10, 19, 37, 67, 94, 73, 43, 22)(11, 20, 38, 68, 95, 74, 44, 23)(12, 21, 39, 69, 96, 75, 45, 24)(28, 52, 82, 56, 29, 53, 83, 55)(30, 54, 84, 57)(34, 61, 80, 66, 36, 63, 81, 64)(35, 62, 79, 65)(40, 70, 76, 46, 41, 71, 78, 48)(42, 72, 77, 47)(58, 85, 91, 100, 106, 98, 103, 88)(59, 86, 93, 102, 107, 97, 104, 89)(60, 87, 92, 101, 108, 99, 105, 90)

(III) Last is Groups&Graphs. Copy everything between (not including) the lines of asterisks into a plain text file and save it as "graph.txt". Then launch G&G (Groups&Graphs) and select Read Text from the File menu.

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&Graph
C4[ 108, 21 ]
108
-1 4 7 9 10
-2 45 70 10 43
-3 4 70 52 54
-4 1 13 3 19
-5 22 24 19 76
-6 13 82 84 76
-7 22 1 16 18
-8 22 40 73 75
-9 1 28 40 30
-10 1 34 2 14
-11 34 40 42 97
-12 100 14 102 97
-13 25 4 37 6
-14 12 46 37 10
-15 56 46 57 25
-16 33 7 31 43
-17 48 94 96 43
-18 55 57 48 7
-19 4 26 5 61
-20 70 104 61 72
-21 26 104 106 107
-22 5 7 8 64
-23 47 48 107 64
-24 91 5 93 107
-25 67 13 15 49
-26 67 19 41 21
-27 49 29 30 41
-28 58 60 9 54
-29 27 106 108 54
-30 55 56 27 9
-31 16 49 51 73
-32 67 78 69 73
-33 78 16 83 84
-34 11 47 91 10
-35 91 70 103 71
-36 47 103 94 95
-37 13 14 80 50
-38 77 89 80 76
-39 89 50 97 98
-40 11 8 9 65
-41 26 27 95 65
-42 11 61 95 63
-43 2 81 16 17
-44 77 78 102 81
-45 2 102 85 86
-46 68 79 14 15
-47 23 34 68 36
-48 23 79 17 18
-49 25 27 94 31
-50 37 71 39 94
-51 71 31 53 54
-52 3 84 85 87
-53 99 51 84 98
-54 3 28 29 51
-55 88 90 18 30
-56 100 101 15 30
-57 15 82 83 18
-58 79 81 28 75
-59 99 68 69 75
-60 99 101 102 28
-61 100 19 20 42
-62 88 78 100 76
-63 88 73 74 42
-64 22 77 23 85
-65 40 41 85 98
-66 77 67 68 98
-67 66 25 26 32
-68 66 46 47 59
-69 59 103 104 32
-70 2 35 3 20
-71 35 50 51 74
-72 80 81 74 20
-73 8 63 31 32
-74 71 93 72 63
-75 58 59 93 8
-76 5 38 6 62
-77 44 66 38 64
-78 33 44 62 32
-79 46 58 48 106
-80 37 38 72 106
-81 44 58 72 43
-82 57 91 92 6
-83 33 57 103 105
-84 33 6 52 53
-85 45 52 64 65
-86 45 105 95 96
-87 105 52 107 108
-88 55 62 63 96
-89 38 39 96 108
-90 55 92 93 108
-91 34 24 35 82
-92 99 90 82 97
-93 24 90 74 75
-94 36 49 17 50
-95 36 41 42 86
-96 88 89 17 86
-97 11 12 92 39
-98 66 39 53 65
-99 59 92 60 53
-100 12 56 61 62
-101 56 60 104 105
-102 44 12 45 60
-103 35 36 69 83
-104 101 69 20 21
-105 101 83 86 87
-106 79 80 29 21
-107 23 24 21 87
-108 89 90 29 87
0

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