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On this page are computer-accessible forms for the graph C4[ 128, 44 ] = SDD({4,4}_4,4).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {64, 121} under the group generated by the following permutations:

a: (13, 48)
b: (27, 58)
c: (62, 64)
d: (19, 22)
e: (2, 26)
f: (6, 25)
g: (1, 2)(3, 5)(4, 7)(6, 9)(8, 12)(10, 15)(11, 17)(13, 20)(14, 19)(16, 24)(18, 27)(21, 31)(22, 29)(23, 34)(25, 37)(26, 39)(28, 40)(30, 42)(32, 45)(33, 47)(35, 48)(36, 50)(38, 51)(41, 53)(43, 52)(44, 54)(46, 58)(49, 59)(55, 60)(56, 62)(57, 61)(63, 64)(66, 68)(67, 70)(69, 73)(72, 77)(74, 80)(76, 82)(78, 85)(79, 84)(81, 88)(83, 91)(86, 94)(87, 95)(89, 98)(92, 101)(93, 102)(97, 106)(99, 109)(100, 105)(103, 110)(104, 113)(107, 116)(108, 112)(111, 115)(114, 121)(118, 120)(119, 122)(124, 125)(126, 127)
h: (9, 37)
m: (52, 55)
n1: (14, 29)
a1: (7, 11)
b1: (3, 38)
c1: (18, 46)
d1: (20, 35)
e1: (30, 49)
f1: (28, 32)
g1: (40, 45)
h1: (21, 41)
m1: (42, 59)
n2: (43, 60)
a2: (34, 50)
b2: (5, 51)
c2: (31, 53)
d2: (3, 4)(5, 7)(8, 10)(11, 51)(12, 15)(13, 14)(16, 47)(17, 38)(18, 23)(19, 20)(22, 35)(24, 33)(27, 34)(28, 30)(29, 48)(32, 49)(36, 46)(40, 42)(43, 44)(45, 59)(50, 58)(52, 54)(55, 57)(60, 61)(66, 67)(68, 70)(71, 75)(72, 74)(76, 81)(77, 80)(78, 79)(82, 88)(83, 87)(84, 85)(89, 97)(90, 96)(91, 95)(92, 93)(98, 106)(99, 107)(100, 105)(101, 102)(103, 104)(108, 115)(109, 116)(110, 113)(111, 112)(117, 123)(118, 122)(119, 120)(124, 127)(125, 126)
e2: (44, 61)
f2: (15, 24)
g2: (10, 16)
h2: (4, 17)
m2: (54, 57)
n3: (2, 3)(4, 6)(7, 10)(9, 13)(11, 16)(12, 18)(14, 21)(15, 20)(17, 25)(19, 28)(22, 32)(23, 30)(24, 35)(26, 38)(29, 41)(31, 43)(33, 46)(36, 49)(37, 48)(40, 52)(44, 56)(45, 55)(53, 60)(61, 63)(65, 66)(67, 69)(68, 71)(70, 74)(72, 76)(73, 78)(75, 81)(77, 83)(79, 86)(80, 85)(82, 89)(84, 92)(87, 93)(88, 96)(90, 99)(91, 98)(94, 103)(95, 105)(97, 107)(100, 108)(101, 110)(102, 112)(104, 114)(106, 115)(109, 117)(111, 119)(113, 120)(116, 122)(118, 124)(121, 125)(123, 127)(126, 128)
a3: (56, 63)
b3: (23, 36)
c3: (8, 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[ 128, 44 ]
128
-1 66 67 69 65
-2 68 70 73 65
-3 66 78 71 74
-4 67 79 72 75
-5 68 80 71 85
-6 69 81 86 76
-7 77 70 84 75
-8 93 72 76 87
-9 88 82 94 73
-10 81 92 83 74
-11 77 70 84 75
-12 77 102 82 95
-13 78 89 103 96
-14 79 90 104 97
-15 88 101 80 91
-16 81 92 83 74
-17 67 79 72 75
-18 89 112 83 105
-19 90 113 84 106
-20 110 85 96 98
-21 99 114 107 86
-22 90 113 84 106
-23 100 111 97 87
-24 88 101 80 91
-25 69 81 86 76
-26 68 70 73 65
-27 100 91 108 98
-28 99 92 115 120
-29 79 90 104 97
-30 93 107 108 119
-31 121 94 116 109
-32 99 92 115 120
-33 77 102 82 95
-34 115 105 95 106
-35 110 85 96 98
-36 100 111 97 87
-37 88 82 94 73
-38 66 78 71 74
-39 66 67 69 65
-40 111 101 118 109
-41 99 114 107 86
-42 122 112 102 116
-43 122 103 125 117
-44 123 104 126 118
-45 111 101 118 109
-46 89 112 83 105
-47 93 72 76 87
-48 78 89 103 96
-49 93 107 108 119
-50 115 105 95 106
-51 68 80 71 85
-52 110 124 117 119
-53 121 94 116 109
-54 123 113 127 120
-55 110 124 117 119
-56 124 114 127 128
-57 123 113 127 120
-58 100 91 108 98
-59 122 112 102 116
-60 122 103 125 117
-61 123 104 126 118
-62 121 125 126 128
-63 124 114 127 128
-64 121 125 126 128
-65 1 2 26 39
-66 1 3 38 39
-67 1 4 17 39
-68 2 26 5 51
-69 1 25 6 39
-70 11 2 26 7
-71 3 5 38 51
-72 47 4 17 8
-73 2 26 37 9
-74 3 16 38 10
-75 11 4 17 7
-76 25 47 6 8
-77 11 33 12 7
-78 13 3 48 38
-79 14 4 17 29
-80 24 15 5 51
-81 25 16 6 10
-82 33 12 37 9
-83 46 16 18 10
-84 11 22 7 19
-85 35 5 51 20
-86 25 6 41 21
-87 23 36 47 8
-88 24 15 37 9
-89 13 46 48 18
-90 22 14 29 19
-91 24 58 15 27
-92 16 28 10 32
-93 47 49 8 30
-94 37 9 31 53
-95 33 12 34 50
-96 13 35 48 20
-97 23 14 36 29
-98 35 58 27 20
-99 28 41 21 32
-100 23 36 58 27
-101 45 24 15 40
-102 33 12 59 42
-103 13 48 60 43
-104 44 14 61 29
-105 34 46 50 18
-106 22 34 50 19
-107 49 30 41 21
-108 58 27 49 30
-109 45 40 31 53
-110 55 35 52 20
-111 23 45 36 40
-112 46 59 18 42
-113 22 57 19 54
-114 56 41 63 21
-115 34 28 50 32
-116 59 31 42 53
-117 55 60 52 43
-118 44 45 61 40
-119 55 49 30 52
-120 57 28 32 54
-121 62 31 53 64
-122 59 60 42 43
-123 44 57 61 54
-124 55 56 52 63
-125 60 62 64 43
-126 44 61 62 64
-127 56 57 63 54
-128 56 62 63 64
0

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