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On this page are computer-accessible forms for the graph C4[ 128, 48 ] = SDD(MSY(4,8,5,4)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {64, 95} under the group generated by the following permutations:

a: (95, 127)
b: (1, 2, 38, 13, 8, 5)(3, 37, 61, 12, 10, 6)(4, 36, 64, 11, 9, 7)(14, 51, 17, 56, 15, 55)(18, 43, 57, 27, 45, 32)(19, 49, 35, 60, 46, 53)(20, 41, 59, 26, 40, 33)(21, 34, 58, 28, 48, 29)(22, 44, 54, 25, 47, 31)(23, 42, 62, 52, 30, 50)(24, 39, 63)(65, 77, 96, 68, 67, 66)(69, 88)(70, 84, 89, 92, 81, 87)(71, 80, 90, 73, 82, 75)(72, 79, 94, 85, 78, 95)(74, 83, 76, 91, 93, 86)(97, 109, 128, 100, 99, 98)(101, 120)(102, 116, 121, 124, 113, 119)(103, 112, 122, 105, 114, 107)(104, 111, 126, 117, 110, 127)(106, 115, 108, 123, 125, 118)
c: (82, 114)
d: (93, 125)
e: (69, 101)
f: (92, 124)
g: (84, 116)
h: (67, 99)
m: (91, 123)
n1: (76, 108)
a1: (65, 97)
b1: (79, 111)
c1: (96, 128)
d1: (81, 113)
e1: (73, 105)
f1: (71, 103)
g1: (2, 3, 4)(5, 6, 7)(8, 14, 62)(9, 18, 59)(10, 19, 63)(11, 17, 44)(12, 15, 46)(13, 16, 28)(20, 57, 41)(21, 54, 39)(22, 58, 42)(23, 35, 34)(24, 37, 43)(25, 64, 55)(26, 38, 51)(27, 61, 56)(29, 33, 32)(30, 50, 53)(36, 49, 52)(40, 47, 48)(67, 70, 94)(68, 69, 93)(71, 90, 79)(72, 89, 80)(73, 96, 88)(74, 95, 87)(77, 84, 85)(78, 83, 86)(99, 102, 126)(100, 101, 125)(103, 122, 111)(104, 121, 112)(105, 128, 120)(106, 127, 119)(109, 116, 117)(110, 115, 118)
h1: (80, 112)
m1: (85, 117)
n2: (78, 110)
a2: (74, 106)
b2: (94, 126)
c2: (86, 118)
d2: (88, 120)
e2: (89, 121)
f2: (70, 102)
g2: (2, 3)(5, 6)(8, 18)(9, 14)(10, 19)(11, 20)(12, 22)(13, 21)(15, 42)(16, 39)(17, 41)(25, 53)(26, 52)(27, 48)(28, 54)(29, 32)(30, 55)(34, 35)(36, 51)(37, 43)(38, 49)(40, 56)(44, 57)(45, 60)(46, 58)(47, 61)(50, 64)(59, 62)(67, 70)(68, 71)(69, 79)(73, 86)(74, 87)(77, 84)(78, 88)(80, 89)(81, 91)(82, 92)(83, 96)(90, 93)(99, 102)(100, 103)(101, 111)(105, 118)(106, 119)(109, 116)(110, 120)(112, 121)(113, 123)(114, 124)(115, 128)(122, 125)
h2: (87, 119)
m2: (2, 4)(6, 7)(9, 10)(11, 13)(14, 62)(15, 46)(16, 44)(17, 28)(18, 63)(19, 59)(20, 64)(21, 50)(22, 33)(23, 61)(24, 38)(25, 57)(26, 37)(27, 35)(29, 58)(30, 54)(31, 60)(32, 42)(34, 56)(36, 52)(39, 53)(40, 48)(41, 55)(43, 51)(69, 93)(70, 94)(71, 95)(72, 96)(73, 89)(74, 90)(75, 91)(76, 92)(77, 85)(78, 86)(79, 87)(80, 88)(101, 125)(102, 126)(103, 127)(104, 128)(105, 121)(106, 122)(107, 123)(108, 124)(109, 117)(110, 118)(111, 119)(112, 120)
n3: (66, 98)
a3: (2, 6)(3, 7)(4, 5)(8, 24)(9, 26)(10, 52)(12, 23)(13, 20)(14, 37)(15, 35)(16, 57)(18, 38)(19, 36)(21, 64)(22, 61)(25, 39)(27, 42)(28, 41)(29, 40)(31, 45)(32, 48)(33, 47)(34, 46)(43, 62)(49, 63)(51, 59)(54, 55)(56, 58)(65, 66)(67, 85)(68, 72)(69, 89)(70, 77)(71, 96)(73, 79)(74, 78)(75, 82)(76, 81)(80, 93)(83, 95)(84, 94)(86, 87)(88, 90)(91, 92)(97, 98)(99, 117)(100, 104)(101, 121)(102, 109)(103, 128)(105, 111)(106, 110)(107, 114)(108, 113)(112, 125)(115, 127)(116, 126)(118, 119)(120, 122)(123, 124)
b3: (83, 115)
c3: (77, 109)
d3: (90, 122)
e3: (72, 104)

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

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