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On this page are computer-accessible forms for the graph C4[ 128, 46 ] = SDD(W(16,2)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {64, 122} under the group generated by the following permutations:

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

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

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