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On this page are computer-accessible forms for the graph C4[ 120, 53 ] = SDD(C_30(1,11)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {60, 61} under the group generated by the following permutations:

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

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

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