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On this page are computer-accessible forms for the graph C4[ 128, 50 ] = BGCG({4,4}_8,0;K1;{12,15}).

(I) Following is a form readable by MAGMA:

g:=Graph<128|{ {64, 69}, {64, 84}, {64, 86}, {64, 107}, {12, 76}, {62, 126}, {34, 98}, {23, 87}, {46, 110}, {13, 76}, {43, 106}, {47, 110}, {56, 121}, {24, 90}, {47, 109}, {48, 114}, {4, 71}, {60, 127}, {33, 98}, {7, 68}, {27, 88}, {44, 111}, {8, 76}, {61, 121}, {32, 100}, {28, 88}, {9, 77}, {13, 73}, {34, 103}, {44, 105}, {48, 117}, {60, 121}, {8, 78}, {26, 92}, {44, 106}, {10, 77}, {14, 73}, {27, 92}, {25, 81}, {49, 121}, {31, 86}, {51, 122}, {9, 67}, {39, 109}, {16, 90}, {20, 94}, {22, 92}, {48, 122}, {23, 92}, {52, 127}, {3, 79}, {34, 110}, {8, 68}, {21, 89}, {41, 101}, {45, 97}, {1, 76}, {61, 112}, {36, 105}, {35, 110}, {56, 117}, {52, 122}, {24, 87}, {2, 82}, {35, 115}, {4, 84}, {54, 102}, {26, 75}, {1, 83}, {38, 116}, {12, 94}, {17, 67}, {25, 75}, {56, 106}, {58, 104}, {1, 82}, {63, 108}, {2, 81}, {3, 80}, {28, 79}, {51, 96}, {56, 107}, {13, 89}, {49, 101}, {53, 97}, {31, 74}, {47, 122}, {49, 100}, {3, 85}, {38, 112}, {36, 114}, {45, 123}, {2, 85}, {37, 114}, {33, 118}, {3, 84}, {17, 73}, {62, 102}, {21, 77}, {43, 115}, {7, 93}, {9, 83}, {15, 85}, {44, 118}, {46, 116}, {50, 104}, {11, 80}, {37, 126}, {12, 87}, {14, 85}, {18, 73}, {22, 77}, {41, 114}, {45, 118}, {52, 111}, {55, 108}, {59, 96}, {11, 87}, {32, 124}, {27, 71}, {6, 91}, {55, 106}, {57, 100}, {5, 91}, {37, 123}, {8, 86}, {16, 78}, {40, 118}, {57, 103}, {24, 120}, {41, 72}, {58, 91}, {19, 113}, {63, 93}, {29, 127}, {23, 117}, {42, 72}, {57, 91}, {14, 109}, {29, 126}, {18, 113}, {20, 119}, {48, 83}, {7, 99}, {35, 71}, {28, 120}, {11, 111}, {13, 105}, {19, 119}, {6, 99}, {29, 120}, {25, 124}, {1, 103}, {16, 119}, {41, 78}, {11, 99}, {20, 124}, {10, 99}, {35, 74}, {17, 120}, {21, 124}, {42, 67}, {21, 127}, {32, 74}, {6, 109}, {63, 84}, {36, 79}, {58, 81}, {5, 105}, {62, 82}, {45, 65}, {16, 125}, {38, 75}, {51, 94}, {55, 90}, {30, 112}, {37, 75}, {36, 74}, {31, 113}, {10, 101}, {61, 82}, {33, 78}, {30, 113}, {14, 97}, {46, 65}, {54, 89}, {33, 81}, {40, 88}, {49, 65}, {50, 66}, {53, 69}, {54, 70}, {2, 115}, {39, 86}, {23, 102}, {50, 67}, {51, 66}, {52, 69}, {55, 70}, {18, 96}, {34, 80}, {30, 108}, {25, 107}, {7, 116}, {27, 104}, {50, 65}, {9, 125}, {43, 95}, {59, 79}, {5, 112}, {40, 93}, {42, 95}, {43, 94}, {47, 90}, {12, 123}, {18, 101}, {22, 97}, {46, 89}, {5, 125}, {39, 95}, {6, 126}, {15, 119}, {60, 68}, {4, 125}, {38, 95}, {31, 102}, {10, 115}, {15, 117}, {17, 107}, {22, 108}, {26, 96}, {42, 80}, {15, 116}, {40, 83}, {19, 104}, {60, 71}, {19, 111}, {62, 66}, {30, 98}, {24, 100}, {57, 69}, {58, 70}, {26, 103}, {63, 66}, {32, 93}, {53, 72}, {59, 70}, {54, 72}, {4, 123}, {39, 88}, {29, 98}, {59, 68}, {20, 128}, {28, 128}, {53, 128}, {61, 128} }>;

(II) A more general form is to represent the graph as the orbit of {64, 69} under the group generated by the following permutations:

a: (2, 13, 34, 9)(3, 21)(4, 25, 36, 29)(5, 33)(6, 45, 38, 41)(7, 53)(8, 57, 40, 61)(10, 14, 46, 42)(11, 22, 15, 54)(12, 26, 48, 62)(16, 58, 44, 30)(17, 35)(18, 47, 50, 43)(19, 55)(20, 59, 52, 63)(24, 27, 56, 31)(28, 60, 64, 32)(39, 49)(65, 95, 101, 109)(66, 94, 96, 122)(67, 115, 73, 110)(68, 69, 93, 128)(70, 111, 108, 119)(71, 107, 74, 120)(72, 99, 97, 116)(75, 114, 126, 123)(76, 103, 83, 82)(77, 85, 89, 80)(78, 91, 118, 112)(79, 127, 84, 124)(81, 105, 98, 125)(86, 100, 88, 121)(87, 92, 117, 102)(90, 104, 106, 113)
b: (2, 9)(3, 17)(4, 25)(5, 33)(6, 41)(7, 49)(8, 57)(11, 18)(12, 26)(13, 34)(14, 42)(15, 50)(16, 58)(20, 27)(21, 35)(22, 43)(23, 51)(24, 59)(29, 36)(30, 44)(31, 52)(32, 60)(38, 45)(39, 53)(40, 61)(47, 54)(48, 62)(56, 63)(65, 116)(66, 117)(67, 85)(68, 100)(69, 86)(70, 90)(71, 124)(72, 109)(73, 80)(74, 127)(75, 123)(76, 103)(77, 115)(78, 91)(79, 120)(81, 125)(82, 83)(84, 107)(87, 96)(88, 128)(89, 110)(92, 94)(93, 121)(95, 97)(98, 105)(99, 101)(102, 122)(104, 119)(106, 108)(111, 113)(112, 118)(114, 126)
c: (2, 34)(4, 36)(6, 38)(8, 40)(9, 13)(10, 46)(11, 15)(12, 48)(14, 42)(16, 44)(18, 50)(20, 52)(22, 54)(24, 56)(25, 29)(26, 62)(27, 31)(28, 64)(30, 58)(32, 60)(41, 45)(43, 47)(57, 61)(59, 63)(65, 101)(66, 96)(67, 73)(68, 93)(69, 128)(70, 108)(71, 74)(72, 97)(75, 126)(76, 83)(77, 89)(78, 118)(79, 84)(80, 85)(81, 98)(82, 103)(86, 88)(87, 117)(90, 106)(91, 112)(92, 102)(94, 122)(95, 109)(99, 116)(100, 121)(104, 113)(105, 125)(107, 120)(110, 115)(111, 119)(114, 123)(124, 127)
d: (2, 57)(3, 53)(4, 45)(5, 33)(6, 25)(7, 21)(8, 13)(9, 40)(10, 32)(11, 20)(14, 64)(15, 52)(16, 44)(17, 39)(18, 31)(22, 63)(23, 51)(24, 43)(26, 62)(27, 50)(28, 42)(29, 38)(34, 61)(35, 49)(36, 41)(46, 60)(47, 56)(54, 59)(65, 71)(66, 92)(67, 88)(68, 89)(69, 85)(72, 79)(73, 86)(74, 101)(75, 126)(77, 93)(78, 105)(80, 128)(81, 91)(82, 103)(84, 97)(87, 94)(90, 106)(95, 120)(96, 102)(98, 112)(99, 124)(100, 115)(107, 109)(110, 121)(111, 119)(116, 127)(117, 122)(118, 125)
e: (1, 2, 33, 34)(3, 8, 35, 40)(4, 39, 36, 7)(5, 6, 37, 38)(9, 14, 41, 46)(10, 45, 42, 13)(11, 12, 43, 44)(15, 16, 47, 48)(17, 18, 49, 50)(19, 24, 51, 56)(20, 55, 52, 23)(21, 22, 53, 54)(25, 30, 57, 62)(26, 61, 58, 29)(27, 28, 59, 60)(31, 32, 63, 64)(65, 67, 73, 101)(66, 107, 113, 100)(68, 71, 88, 79)(69, 102, 124, 108)(70, 127, 92, 128)(72, 89, 77, 97)(74, 93, 84, 86)(75, 112, 91, 126)(76, 115, 118, 80)(78, 110, 83, 85)(81, 98, 103, 82)(87, 94, 106, 111)(90, 122, 117, 119)(95, 105, 99, 123)(96, 121, 104, 120)(109, 114, 116, 125)

(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.

**************

&Graph
C4[ 128, 50 ]
128
-1 103 82 83 76
-2 81 82 115 85
-3 79 80 84 85
-4 123 125 71 84
-5 112 91 125 105
-6 99 91 126 109
-7 99 68 93 116
-8 78 68 86 76
-9 77 67 125 83
-10 77 99 101 115
-11 99 111 80 87
-12 123 94 76 87
-13 89 105 73 76
-14 73 85 97 109
-15 116 117 85 119
-16 78 90 125 119
-17 67 73 107 120
-18 101 113 73 96
-19 111 113 104 119
-20 124 94 128 119
-21 77 89 124 127
-22 77 92 97 108
-23 102 92 117 87
-24 100 90 87 120
-25 124 81 107 75
-26 92 103 96 75
-27 88 92 71 104
-28 88 79 128 120
-29 126 127 98 120
-30 112 113 108 98
-31 102 113 74 86
-32 100 124 93 74
-33 78 81 118 98
-34 110 80 103 98
-35 110 71 115 74
-36 79 114 105 74
-37 123 114 126 75
-38 112 116 95 75
-39 88 95 86 109
-40 88 93 83 118
-41 78 101 114 72
-42 67 80 72 95
-43 115 94 95 106
-44 111 105 106 118
-45 123 118 97 65
-46 110 89 116 65
-47 110 122 90 109
-48 122 114 83 117
-49 121 100 101 65
-50 66 67 104 65
-51 66 122 94 96
-52 111 122 69 127
-53 69 72 128 97
-54 89 102 70 72
-55 90 70 106 108
-56 121 106 117 107
-57 100 69 91 103
-58 91 70 81 104
-59 68 79 70 96
-60 121 68 71 127
-61 121 112 82 128
-62 66 102 82 126
-63 66 93 84 108
-64 69 84 107 86
-65 45 46 49 50
-66 50 51 62 63
-67 17 50 9 42
-68 59 60 7 8
-69 57 52 53 64
-70 55 58 59 54
-71 35 4 27 60
-72 41 42 53 54
-73 13 14 17 18
-74 35 36 31 32
-75 25 26 37 38
-76 1 12 13 8
-77 22 9 10 21
-78 33 16 8 41
-79 3 36 59 28
-80 11 34 3 42
-81 33 2 25 58
-82 1 2 61 62
-83 1 48 40 9
-84 3 4 63 64
-85 2 3 14 15
-86 39 8 31 64
-87 11 12 23 24
-88 27 28 39 40
-89 13 46 21 54
-90 55 24 47 16
-91 57 58 5 6
-92 22 23 26 27
-93 7 40 63 32
-94 12 51 20 43
-95 38 39 42 43
-96 26 59 18 51
-97 22 45 14 53
-98 33 34 29 30
-99 11 6 7 10
-100 24 57 49 32
-101 49 18 41 10
-102 23 62 31 54
-103 1 34 57 26
-104 58 27 50 19
-105 44 13 36 5
-106 44 55 56 43
-107 56 25 17 64
-108 22 55 30 63
-109 14 47 6 39
-110 34 35 46 47
-111 11 44 19 52
-112 5 38 61 30
-113 18 19 30 31
-114 36 37 48 41
-115 2 35 10 43
-116 46 15 38 7
-117 23 56 15 48
-118 33 44 45 40
-119 15 16 19 20
-120 24 17 28 29
-121 56 49 60 61
-122 47 48 51 52
-123 12 45 4 37
-124 25 20 21 32
-125 4 5 16 9
-126 37 6 29 62
-127 60 29 52 21
-128 28 61 20 53
0

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