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On this page are computer-accessible forms for the graph C4[ 128, 45 ] = SDD(MPS(4,16;3)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {64, 68} under the group generated by the following permutations:

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

(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.

**************

&Graph
C4[ 128, 45 ]
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 86
-6 69 81 76 87
-7 77 88 70 82
-8 89 72 76 98
-9 99 90 83 73
-10 100 91 84 74
-11 101 92 85 75
-12 77 102 83 98
-13 78 103 93 97
-14 111 79 104 94
-15 80 105 95 96
-16 112 81 106 96
-17 113 82 107 97
-18 89 93 84 109
-19 94 85 86 108
-20 110 114 105 87
-21 88 103 115 119
-22 100 90 116 120
-23 99 121 91 117
-24 110 122 92 118
-25 102 95 108 109
-26 101 123 114 126
-27 112 124 104 127
-28 111 125 106 128
-29 125 117 107 118
-30 121 113 124 126
-31 123 115 127 120
-32 122 116 128 119
-33 125 117 107 118
-34 122 116 128 119
-35 123 115 127 120
-36 121 113 124 126
-37 110 122 92 118
-38 111 125 106 128
-39 112 124 104 127
-40 101 123 114 126
-41 113 82 107 97
-42 99 121 91 117
-43 100 90 116 120
-44 88 103 115 119
-45 101 92 85 75
-46 110 114 105 87
-47 112 81 106 96
-48 111 79 104 94
-49 77 88 70 82
-50 78 103 93 97
-51 100 91 84 74
-52 99 90 83 73
-53 67 79 72 75
-54 94 85 86 108
-55 80 105 95 96
-56 69 81 76 87
-57 68 70 73 65
-58 77 102 83 98
-59 89 93 84 109
-60 66 78 71 74
-61 66 67 69 65
-62 89 72 76 98
-63 102 95 108 109
-64 68 80 71 86
-65 1 2 57 61
-66 1 3 60 61
-67 1 4 61 53
-68 2 57 5 64
-69 1 56 6 61
-70 2 57 49 7
-71 3 5 60 64
-72 4 62 8 53
-73 2 57 52 9
-74 3 60 51 10
-75 11 45 4 53
-76 56 6 62 8
-77 12 58 49 7
-78 13 3 60 50
-79 14 4 48 53
-80 55 15 5 64
-81 56 47 16 6
-82 49 17 7 41
-83 12 58 52 9
-84 59 18 51 10
-85 11 45 19 54
-86 5 19 64 54
-87 56 46 6 20
-88 44 49 7 21
-89 59 18 62 8
-90 22 52 9 43
-91 23 51 42 10
-92 11 45 24 37
-93 13 59 50 18
-94 14 48 19 54
-95 55 25 15 63
-96 55 47 15 16
-97 13 17 50 41
-98 12 58 62 8
-99 23 52 9 42
-100 22 51 10 43
-101 11 45 26 40
-102 12 25 58 63
-103 44 13 50 21
-104 14 48 27 39
-105 55 46 15 20
-106 47 16 38 28
-107 33 17 29 41
-108 25 19 63 54
-109 25 59 18 63
-110 24 46 37 20
-111 14 48 38 28
-112 47 16 27 39
-113 36 17 30 41
-114 46 26 40 20
-115 44 35 31 21
-116 22 34 32 43
-117 33 23 29 42
-118 33 24 37 29
-119 44 34 21 32
-120 22 35 31 43
-121 23 36 30 42
-122 34 24 37 32
-123 35 26 40 31
-124 36 27 39 30
-125 33 38 28 29
-126 36 26 40 30
-127 35 27 39 31
-128 34 38 28 32
0

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