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On this page are computer-accessible forms for the graph C4[ 120, 61 ] = SDD(PS(6,5;2)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {12, 63} under the group generated by the following permutations:

a: (86, 116)
b: (87, 117)
c: (88, 118)
d: (2, 3, 4)(5, 33, 53)(6, 28, 49)(7, 29, 54)(8, 34, 48)(9, 23, 24)(10, 38, 26)(11, 22, 39)(12, 37, 40)(13, 18, 50)(14, 20, 56)(15, 17, 41)(16, 19, 55)(21, 42, 59)(25, 27, 32)(30, 57, 60)(35, 43, 44)(36, 58, 46)(45, 47, 52)(62, 72, 82)(63, 74, 75)(64, 65, 83)(66, 76, 86)(68, 69, 80)(70, 88, 89)(73, 84, 85)(78, 79, 90)(92, 102, 112)(93, 104, 105)(94, 95, 113)(96, 106, 116)(98, 99, 110)(100, 118, 119)(103, 114, 115)(108, 109, 120)
e: (83, 113)
f: (69, 99)
g: (67, 97)
h: (65, 95)
m: (68, 98)
n1: (72, 102)
a1: (85, 115)
b1: (74, 104)
c1: (79, 109)
d1: (62, 92)
e1: (71, 101)
f1: (61, 91)
g1: (84, 114)
h1: (63, 93)
m1: (73, 103)
n2: (76, 106)
a2: (70, 100)
b2: (81, 111)
c2: (2, 24)(3, 23)(4, 9)(5, 53)(6, 15)(7, 11)(8, 59)(10, 56)(12, 60)(14, 26)(16, 25)(17, 49)(18, 50)(19, 32)(20, 38)(21, 48)(22, 54)(27, 55)(28, 41)(29, 39)(30, 40)(31, 51)(34, 42)(35, 47)(37, 57)(43, 45)(44, 52)(46, 58)(61, 67)(62, 86)(63, 89)(64, 68)(65, 80)(66, 82)(69, 83)(70, 75)(71, 87)(72, 76)(73, 79)(74, 88)(77, 81)(78, 84)(85, 90)(91, 97)(92, 116)(93, 119)(94, 98)(95, 110)(96, 112)(99, 113)(100, 105)(101, 117)(102, 106)(103, 109)(104, 118)(107, 111)(108, 114)(115, 120)
d2: (89, 119)
e2: (77, 107)
f2: (3, 4)(5, 53)(6, 48)(7, 54)(8, 49)(9, 23)(10, 37)(11, 22)(12, 38)(13, 36)(14, 30)(15, 21)(16, 35)(17, 59)(18, 46)(19, 44)(20, 60)(25, 47)(26, 40)(27, 45)(28, 34)(31, 51)(32, 52)(41, 42)(43, 55)(50, 58)(56, 57)(62, 82)(63, 74)(64, 73)(65, 85)(66, 86)(68, 79)(69, 78)(71, 81)(77, 87)(80, 90)(83, 84)(88, 89)(92, 112)(93, 104)(94, 103)(95, 115)(96, 116)(98, 109)(99, 108)(101, 111)(107, 117)(110, 120)(113, 114)(118, 119)
g2: (1, 2, 4)(5, 39, 15)(6, 26, 13)(7, 24, 14)(8, 40, 16)(9, 30, 56)(10, 35, 50)(11, 21, 41)(12, 36, 55)(17, 42, 53)(18, 43, 49)(19, 58, 48)(20, 57, 54)(22, 33, 59)(23, 29, 60)(27, 31, 32)(28, 44, 38)(34, 46, 37)(47, 51, 52)(62, 75, 64)(63, 73, 83)(65, 84, 82)(66, 76, 86)(67, 70, 89)(69, 77, 80)(72, 85, 74)(79, 87, 90)(92, 105, 94)(93, 103, 113)(95, 114, 112)(96, 106, 116)(97, 100, 119)(99, 107, 110)(102, 115, 104)(109, 117, 120)
h2: (66, 96)
m2: (80, 110)
n3: (90, 120)
a3: (82, 112)
b3: (75, 105)
c3: (78, 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, 61 ]
120
-1 67 91 61 97
-2 100 91 70 61
-3 88 91 61 118
-4 89 91 61 119
-5 66 92 62 96
-6 68 92 62 98
-7 89 92 62 119
-8 90 92 62 120
-9 67 93 63 97
-10 99 69 93 63
-11 93 116 63 86
-12 90 93 63 120
-13 68 94 64 98
-14 100 70 94 64
-15 94 116 64 86
-16 94 117 64 87
-17 66 95 96 65
-18 99 69 95 65
-19 95 117 65 87
-20 88 95 118 65
-21 66 103 73 96
-22 66 104 74 96
-23 67 104 74 97
-24 67 105 75 97
-25 68 101 71 98
-26 68 105 75 98
-27 99 101 69 71
-28 99 69 102 72
-29 100 102 70 72
-30 100 70 103 73
-31 77 101 71 107
-32 110 101 80 71
-33 102 72 106 76
-34 78 102 72 108
-35 77 103 73 107
-36 79 103 73 109
-37 78 104 74 108
-38 110 80 104 74
-39 105 106 75 76
-40 79 105 75 109
-41 113 83 106 76
-42 114 84 106 76
-43 77 114 84 107
-44 77 115 85 107
-45 78 111 81 108
-46 78 115 85 108
-47 111 79 81 109
-48 79 112 82 109
-49 110 112 80 82
-50 110 80 113 83
-51 111 81 117 87
-52 111 90 81 120
-53 112 82 116 86
-54 88 112 82 118
-55 113 83 117 87
-56 89 113 83 119
-57 88 114 84 118
-58 90 114 84 120
-59 115 116 85 86
-60 89 115 85 119
-61 1 2 3 4
-62 5 6 7 8
-63 11 12 9 10
-64 13 14 15 16
-65 17 18 19 20
-66 22 5 17 21
-67 1 23 24 9
-68 13 25 26 6
-69 27 28 18 10
-70 2 14 29 30
-71 25 27 31 32
-72 33 34 28 29
-73 35 36 30 21
-74 22 23 37 38
-75 24 26 39 40
-76 33 39 41 42
-77 44 35 31 43
-78 34 45 46 37
-79 36 47 48 40
-80 38 49 50 32
-81 45 47 51 52
-82 48 49 53 54
-83 55 56 50 41
-84 57 58 42 43
-85 44 46 59 60
-86 11 15 59 53
-87 55 16 51 19
-88 57 3 20 54
-89 56 4 60 7
-90 12 58 8 52
-91 1 2 3 4
-92 5 6 7 8
-93 11 12 9 10
-94 13 14 15 16
-95 17 18 19 20
-96 22 5 17 21
-97 1 23 24 9
-98 13 25 26 6
-99 27 28 18 10
-100 2 14 29 30
-101 25 27 31 32
-102 33 34 28 29
-103 35 36 30 21
-104 22 23 37 38
-105 24 26 39 40
-106 33 39 41 42
-107 44 35 31 43
-108 34 45 46 37
-109 36 47 48 40
-110 38 49 50 32
-111 45 47 51 52
-112 48 49 53 54
-113 55 56 50 41
-114 57 58 42 43
-115 44 46 59 60
-116 11 15 59 53
-117 55 16 51 19
-118 57 3 20 54
-119 56 4 60 7
-120 12 58 8 52
0

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