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On this page are computer-accessible forms for the graph C4[ 120, 65 ] = BGCG(Pr_10(2,3,1,4);K2;{2,3}).

(I) Following is a form readable by MAGMA:

g:=Graph<120|{ {51, 63}, {50, 61}, {46, 62}, {40, 61}, {41, 63}, {39, 62}, {20, 62}, {16, 61}, {9, 61}, {10, 62}, {7, 63}, {5, 63}, {18, 82}, {45, 109}, {24, 88}, {21, 85}, {8, 73}, {48, 113}, {13, 76}, {11, 74}, {9, 75}, {58, 120}, {49, 115}, {29, 95}, {22, 84}, {12, 78}, {31, 93}, {32, 98}, {40, 106}, {4, 71}, {24, 91}, {10, 73}, {37, 102}, {28, 88}, {44, 104}, {2, 71}, {53, 112}, {47, 106}, {4, 65}, {38, 99}, {27, 93}, {49, 119}, {41, 111}, {6, 65}, {27, 92}, {15, 72}, {36, 99}, {59, 115}, {39, 110}, {47, 102}, {40, 98}, {43, 97}, {11, 64}, {59, 112}, {15, 68}, {32, 107}, {7, 75}, {52, 120}, {25, 85}, {17, 93}, {16, 92}, {8, 68}, {18, 95}, {34, 111}, {42, 103}, {20, 90}, {26, 84}, {3, 83}, {48, 96}, {21, 69}, {6, 86}, {31, 79}, {39, 119}, {1, 80}, {20, 69}, {30, 79}, {36, 117}, {5, 87}, {59, 105}, {26, 72}, {32, 114}, {17, 66}, {52, 103}, {30, 77}, {18, 70}, {23, 67}, {14, 91}, {57, 108}, {49, 100}, {21, 64}, {33, 116}, {35, 118}, {7, 81}, {14, 89}, {54, 97}, {24, 79}, {35, 116}, {15, 87}, {60, 100}, {27, 67}, {42, 114}, {3, 90}, {60, 101}, {23, 78}, {20, 77}, {8, 82}, {55, 109}, {49, 107}, {28, 70}, {11, 80}, {59, 96}, {46, 117}, {23, 76}, {13, 86}, {22, 74}, {42, 118}, {3, 94}, {56, 101}, {4, 89}, {13, 83}, {55, 105}, {28, 66}, {1, 94}, {55, 104}, {51, 108}, {14, 81}, {18, 114}, {43, 75}, {34, 66}, {41, 73}, {15, 110}, {55, 86}, {54, 87}, {48, 81}, {22, 119}, {6, 100}, {57, 91}, {7, 101}, {40, 74}, {2, 97}, {10, 105}, {35, 64}, {9, 109}, {12, 104}, {37, 64}, {51, 86}, {38, 67}, {16, 118}, {54, 80}, {36, 66}, {41, 79}, {19, 116}, {57, 94}, {56, 95}, {52, 83}, {42, 77}, {32, 72}, {14, 103}, {29, 116}, {37, 76}, {34, 72}, {54, 92}, {45, 71}, {10, 97}, {56, 83}, {50, 89}, {28, 119}, {19, 120}, {39, 76}, {1, 109}, {60, 80}, {8, 100}, {38, 74}, {58, 87}, {2, 108}, {47, 65}, {45, 67}, {31, 113}, {13, 98}, {3, 115}, {44, 92}, {27, 107}, {19, 99}, {16, 96}, {6, 118}, {5, 117}, {9, 120}, {53, 68}, {47, 94}, {46, 95}, {31, 110}, {36, 85}, {29, 111}, {60, 78}, {1, 114}, {25, 106}, {2, 113}, {4, 112}, {50, 70}, {17, 101}, {33, 84}, {51, 70}, {48, 69}, {46, 91}, {45, 88}, {5, 115}, {44, 90}, {25, 110}, {29, 106}, {37, 82}, {38, 81}, {17, 105}, {53, 77}, {23, 111}, {30, 102}, {33, 89}, {34, 90}, {12, 117}, {24, 98}, {26, 96}, {11, 112}, {58, 65}, {35, 88}, {26, 102}, {50, 78}, {33, 93}, {12, 113}, {57, 68}, {52, 73}, {30, 99}, {21, 107}, {53, 75}, {44, 82}, {43, 85}, {25, 103}, {22, 104}, {19, 108}, {58, 69}, {56, 71}, {43, 84} }>;

(II) A more general form is to represent the graph as the orbit of {51, 63} under the group generated by the following permutations:

a: (1, 31)(2, 32)(3, 33)(4, 34)(5, 35)(6, 36)(7, 37)(8, 38)(9, 39)(10, 40)(11, 41)(12, 42)(13, 43)(14, 44)(15, 45)(16, 46)(17, 47)(18, 48)(19, 49)(20, 50)(21, 51)(22, 52)(23, 53)(24, 54)(25, 55)(26, 56)(27, 57)(28, 58)(29, 59)(30, 60)(61, 62)(63, 64)(65, 66)(67, 68)(69, 70)(71, 72)(73, 74)(75, 76)(77, 78)(79, 80)(81, 82)(83, 84)(85, 86)(87, 88)(89, 90)(91, 92)(93, 94)(95, 96)(97, 98)(99, 100)(101, 102)(103, 104)(105, 106)(107, 108)(109, 110)(111, 112)(113, 114)(115, 116)(117, 118)(119, 120)
b: (2, 24, 27, 15)(3, 9, 18, 11)(4, 13, 16, 8)(5, 19, 28, 21)(7, 29, 22, 20)(10, 14, 23, 26)(12, 30, 17, 25)(32, 54, 57, 45)(33, 39, 48, 41)(34, 43, 46, 38)(35, 49, 58, 51)(37, 59, 52, 50)(40, 44, 53, 56)(42, 60, 47, 55)(61, 82, 112, 83)(62, 81, 111, 84)(63, 116, 119, 69)(64, 115, 120, 70)(65, 86, 118, 100)(66, 85, 117, 99)(67, 72, 97, 91)(68, 71, 98, 92)(73, 89, 76, 96)(74, 90, 75, 95)(77, 101, 106, 104)(78, 102, 105, 103)(79, 93, 110, 113)(80, 94, 109, 114)(87, 108, 88, 107)
c: (1, 2, 27, 15)(3, 4, 17, 26)(5, 11, 10, 16)(6, 7, 22, 20)(8, 9, 12, 21)(13, 14, 28, 30)(18, 19, 23, 25)(31, 32, 57, 45)(33, 34, 47, 56)(35, 41, 40, 46)(36, 37, 52, 50)(38, 39, 42, 51)(43, 44, 58, 60)(48, 49, 53, 55)(61, 117, 64, 73)(62, 118, 63, 74)(65, 101, 84, 90)(66, 102, 83, 89)(67, 110, 114, 108)(68, 109, 113, 107)(69, 100, 75, 104)(70, 99, 76, 103)(71, 93, 72, 94)(77, 86, 81, 119)(78, 85, 82, 120)(79, 98, 91, 88)(80, 97, 92, 87)(95, 116, 111, 106)(96, 115, 112, 105)
d: (1, 3)(2, 26)(4, 15)(5, 11)(6, 8)(7, 21)(9, 20)(10, 16)(12, 22)(13, 18)(14, 25)(17, 27)(19, 30)(23, 28)(24, 29)(31, 33)(32, 56)(34, 45)(35, 41)(36, 38)(37, 51)(39, 50)(40, 46)(42, 52)(43, 48)(44, 55)(47, 57)(49, 60)(53, 58)(54, 59)(61, 62)(63, 64)(65, 68)(66, 67)(69, 75)(70, 76)(71, 72)(73, 118)(74, 117)(77, 120)(78, 119)(79, 116)(80, 115)(81, 85)(82, 86)(83, 114)(84, 113)(87, 112)(88, 111)(89, 110)(90, 109)(91, 106)(92, 105)(95, 98)(96, 97)(101, 107)(102, 108)

(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[ 120, 65 ]
120
-1 80 114 94 109
-2 113 71 97 108
-3 90 115 83 94
-4 89 112 71 65
-5 115 117 63 87
-6 100 118 86 65
-7 101 81 63 75
-8 100 68 82 73
-9 61 75 109 120
-10 105 62 73 97
-11 112 80 74 64
-12 78 113 104 117
-13 83 86 76 98
-14 89 91 81 103
-15 110 68 72 87
-16 92 61 96 118
-17 66 101 93 105
-18 70 114 82 95
-19 99 116 108 120
-20 77 90 69 62
-21 69 85 107 64
-22 104 84 74 119
-23 67 78 111 76
-24 88 79 91 98
-25 110 103 106 85
-26 102 72 84 96
-27 67 92 93 107
-28 66 88 70 119
-29 111 116 95 106
-30 77 99 79 102
-31 110 79 113 93
-32 114 72 107 98
-33 89 93 116 84
-34 66 111 90 72
-35 88 116 118 64
-36 66 99 117 85
-37 102 82 64 76
-38 99 67 81 74
-39 110 62 119 76
-40 61 106 74 98
-41 111 79 73 63
-42 77 103 114 118
-43 84 85 75 97
-44 90 92 82 104
-45 88 67 71 109
-46 91 62 95 117
-47 102 94 106 65
-48 69 113 81 96
-49 100 115 107 119
-50 78 89 70 61
-51 70 63 86 108
-52 103 83 73 120
-53 77 68 112 75
-54 80 92 97 87
-55 104 105 86 109
-56 101 71 83 95
-57 68 91 94 108
-58 69 65 87 120
-59 112 115 105 96
-60 78 100 101 80
-61 16 50 40 9
-62 46 39 20 10
-63 5 7 51 41
-64 11 35 37 21
-65 47 58 4 6
-66 34 36 17 28
-67 23 45 27 38
-68 57 15 8 53
-69 58 48 20 21
-70 28 50 18 51
-71 45 56 2 4
-72 34 15 26 32
-73 8 41 52 10
-74 11 22 38 40
-75 7 9 53 43
-76 23 13 37 39
-77 30 20 42 53
-78 12 23 60 50
-79 24 30 41 31
-80 11 1 60 54
-81 14 48 38 7
-82 44 37 18 8
-83 56 13 3 52
-84 22 33 26 43
-85 25 36 21 43
-86 55 13 6 51
-87 58 15 5 54
-88 45 24 35 28
-89 33 14 4 50
-90 44 34 3 20
-91 24 46 57 14
-92 44 16 27 54
-93 33 27 17 31
-94 1 57 3 47
-95 56 46 18 29
-96 26 48 59 16
-97 2 10 43 54
-98 13 24 40 32
-99 36 38 19 30
-100 49 60 6 8
-101 56 60 17 7
-102 47 26 37 30
-103 14 25 52 42
-104 22 44 55 12
-105 55 59 17 10
-106 25 47 29 40
-107 27 49 21 32
-108 2 57 51 19
-109 55 1 45 9
-110 25 15 39 31
-111 23 34 29 41
-112 11 4 59 53
-113 12 2 48 31
-114 1 18 42 32
-115 3 59 5 49
-116 33 35 29 19
-117 12 46 36 5
-118 35 16 6 42
-119 22 49 28 39
-120 58 19 52 9
0

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