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On this page are computer-accessible forms for the graph C4[ 120, 62 ] = BGCG(PS(6,5;2);K2;{4,5}).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {56, 61} under the group generated by the following permutations:

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

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

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