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On this page are computer-accessible forms for the graph C4[ 136, 14 ] = SDD(W(17,2)).

(I) Following is a form readable by MAGMA:

g:=Graph<136|{ {64, 97}, {68, 101}, {66, 99}, {64, 98}, {68, 102}, {65, 99}, {65, 98}, {66, 100}, {67, 101}, {67, 100}, {6, 70}, {30, 94}, {8, 72}, {4, 69}, {7, 70}, {5, 71}, {11, 73}, {5, 70}, {34, 97}, {11, 72}, {28, 95}, {56, 123}, {60, 127}, {1, 69}, {36, 96}, {12, 72}, {14, 74}, {24, 92}, {51, 119}, {56, 124}, {57, 125}, {58, 126}, {59, 127}, {13, 72}, {50, 119}, {57, 124}, {59, 126}, {3, 69}, {39, 97}, {15, 73}, {27, 93}, {48, 118}, {1, 70}, {37, 98}, {2, 69}, {14, 73}, {25, 94}, {49, 118}, {58, 125}, {18, 90}, {42, 98}, {50, 120}, {16, 91}, {40, 99}, {22, 93}, {46, 101}, {52, 120}, {54, 122}, {55, 123}, {10, 71}, {52, 121}, {53, 120}, {55, 122}, {9, 71}, {21, 91}, {45, 99}, {8, 71}, {19, 92}, {43, 100}, {54, 121}, {6, 86}, {35, 115}, {33, 113}, {30, 78}, {28, 77}, {35, 114}, {32, 113}, {31, 78}, {29, 79}, {38, 116}, {32, 114}, {10, 89}, {34, 113}, {29, 78}, {53, 102}, {3, 87}, {39, 115}, {12, 88}, {24, 76}, {26, 78}, {48, 100}, {25, 76}, {38, 115}, {15, 89}, {36, 114}, {27, 77}, {51, 101}, {2, 85}, {37, 114}, {13, 90}, {26, 77}, {49, 102}, {18, 74}, {20, 76}, {45, 117}, {47, 119}, {16, 73}, {19, 74}, {44, 117}, {47, 118}, {17, 75}, {23, 77}, {44, 118}, {17, 74}, {40, 115}, {23, 76}, {46, 117}, {41, 117}, {22, 75}, {41, 116}, {9, 87}, {42, 116}, {21, 75}, {62, 96}, {63, 97}, {7, 88}, {20, 75}, {43, 116}, {63, 96}, {9, 105}, {11, 107}, {8, 105}, {11, 106}, {54, 87}, {56, 89}, {58, 91}, {60, 93}, {62, 95}, {4, 102}, {8, 106}, {14, 108}, {52, 86}, {56, 90}, {57, 91}, {60, 94}, {61, 95}, {4, 103}, {10, 105}, {52, 87}, {53, 86}, {57, 90}, {61, 94}, {3, 103}, {15, 107}, {27, 127}, {48, 84}, {50, 86}, {2, 103}, {14, 107}, {49, 84}, {1, 103}, {12, 106}, {24, 126}, {51, 85}, {58, 92}, {59, 93}, {13, 106}, {50, 85}, {59, 92}, {21, 125}, {1, 104}, {22, 127}, {26, 112}, {5, 105}, {29, 113}, {5, 104}, {34, 79}, {16, 125}, {19, 126}, {29, 112}, {6, 104}, {33, 79}, {30, 112}, {18, 124}, {54, 88}, {55, 89}, {7, 104}, {32, 79}, {31, 112}, {55, 88}, {9, 121}, {32, 80}, {10, 123}, {13, 124}, {35, 81}, {28, 111}, {35, 80}, {15, 123}, {38, 82}, {36, 80}, {27, 111}, {2, 119}, {37, 80}, {26, 111}, {12, 122}, {39, 81}, {24, 110}, {25, 110}, {38, 81}, {21, 109}, {42, 82}, {23, 111}, {44, 84}, {20, 109}, {40, 81}, {23, 110}, {43, 82}, {3, 121}, {41, 83}, {20, 110}, {47, 85}, {16, 107}, {41, 82}, {22, 109}, {47, 84}, {17, 109}, {7, 122}, {17, 108}, {46, 83}, {6, 120}, {33, 95}, {18, 108}, {45, 83}, {19, 108}, {31, 96}, {44, 83}, {4, 136}, {25, 128}, {28, 129}, {31, 130}, {30, 128}, {33, 129}, {34, 131}, {37, 132}, {39, 131}, {36, 130}, {45, 133}, {46, 135}, {40, 133}, {43, 134}, {42, 132}, {51, 135}, {48, 134}, {49, 136}, {60, 128}, {61, 129}, {62, 130}, {63, 131}, {53, 136}, {61, 128}, {63, 130}, {62, 129}, {64, 131}, {68, 135}, {64, 132}, {67, 135}, {66, 134}, {65, 133}, {65, 132}, {67, 134}, {66, 133}, {68, 136} }>;

(II) A more general form is to represent the graph as the orbit of {64, 97} under the group generated by the following permutations:

a: (102, 136)
b: (38, 40)(41, 45)(42, 65)(43, 66)(82, 99)(116, 133)
c: (95, 129)
d: (2, 4)(47, 49)(50, 53)(51, 68)(85, 102)(119, 136)
e: (99, 133)
f: (2, 5)(3, 6)(4, 7)(8, 47)(9, 50)(10, 51)(11, 44)(12, 49)(13, 48)(14, 41)(15, 46)(16, 45)(17, 38)(18, 43)(19, 42)(20, 35)(21, 40)(22, 39)(23, 32)(24, 37)(25, 36)(26, 29)(27, 34)(28, 33)(30, 31)(53, 54)(55, 68)(56, 67)(57, 66)(58, 65)(59, 64)(60, 63)(61, 62)(69, 70)(71, 85)(72, 84)(73, 83)(74, 82)(75, 81)(76, 80)(77, 79)(86, 87)(88, 102)(89, 101)(90, 100)(91, 99)(92, 98)(93, 97)(94, 96)(103, 104)(105, 119)(106, 118)(107, 117)(108, 116)(109, 115)(110, 114)(111, 113)(120, 121)(122, 136)(123, 135)(124, 134)(125, 133)(126, 132)(127, 131)(128, 130)
g: (41, 43)(44, 48)(45, 66)(46, 67)(83, 100)(117, 134)
h: (20, 22)(23, 27)(24, 59)(25, 60)(76, 93)(110, 127)
m: (26, 28)(29, 33)(30, 61)(31, 62)(78, 95)(112, 129)
n1: (17, 19)(20, 24)(21, 58)(22, 59)(75, 92)(109, 126)
a1: (97, 131)
b1: (93, 127)
c1: (32, 34)(35, 39)(36, 63)(37, 64)(80, 97)(114, 131)
d1: (96, 130)
e1: (14, 16)(17, 21)(18, 57)(19, 58)(74, 91)(108, 125)
f1: (70, 104)
g1: (11, 13)(14, 18)(15, 56)(16, 57)(73, 90)(107, 124)
h1: (92, 126)
m1: (101, 135)
n2: (90, 124)
a2: (35, 37)(38, 42)(39, 64)(40, 65)(81, 98)(115, 132)
b2: (94, 128)
c2: (91, 125)
d2: (86, 120)
e2: (98, 132)
f2: (29, 31)(32, 36)(33, 62)(34, 63)(79, 96)(113, 130)
g2: (44, 46)(47, 51)(48, 67)(49, 68)(84, 101)(118, 135)
h2: (87, 121)
m2: (89, 123)
n3: (100, 134)
a3: (1, 2, 47, 44, 41, 38, 35, 32, 29, 26, 23, 20, 17, 14, 11, 8, 5)(3, 50, 49, 46, 43, 40, 37, 34, 31, 28, 25, 22, 19, 16, 13, 10, 7)(4, 51, 48, 45, 42, 39, 36, 33, 30, 27, 24, 21, 18, 15, 12, 9, 6)(52, 53, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54)(69, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70)(86, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87)(103, 119, 118, 117, 116, 115, 114, 113, 112, 111, 110, 109, 108, 107, 106, 105, 104)(120, 136, 135, 134, 133, 132, 131, 130, 129, 128, 127, 126, 125, 124, 123, 122, 121)
b3: (88, 122)
c3: (23, 25)(26, 30)(27, 60)(28, 61)(77, 94)(111, 128)
d3: (8, 10)(11, 15)(12, 55)(13, 56)(72, 89)(106, 123)
e3: (69, 103)

(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[ 136, 14 ]
136
-1 69 70 103 104
-2 69 103 85 119
-3 121 69 103 87
-4 69 102 103 136
-5 70 71 104 105
-6 70 104 86 120
-7 88 122 70 104
-8 71 72 105 106
-9 121 71 105 87
-10 89 123 71 105
-11 72 73 106 107
-12 88 122 72 106
-13 90 124 72 106
-14 73 74 107 108
-15 89 123 73 107
-16 91 125 73 107
-17 74 75 108 109
-18 90 124 74 108
-19 92 126 74 108
-20 110 75 76 109
-21 91 125 75 109
-22 93 127 75 109
-23 77 110 111 76
-24 110 92 126 76
-25 110 94 128 76
-26 77 78 111 112
-27 77 111 93 127
-28 77 111 95 129
-29 78 79 112 113
-30 78 112 94 128
-31 78 112 96 130
-32 79 80 113 114
-33 79 113 95 129
-34 79 113 97 131
-35 80 81 114 115
-36 80 114 96 130
-37 132 80 114 98
-38 81 82 115 116
-39 81 115 97 131
-40 99 133 81 115
-41 82 83 116 117
-42 132 82 116 98
-43 100 134 82 116
-44 83 84 117 118
-45 99 133 83 117
-46 101 135 83 117
-47 84 85 118 119
-48 100 134 84 118
-49 102 136 84 118
-50 85 86 119 120
-51 101 135 85 119
-52 121 86 87 120
-53 102 136 86 120
-54 88 121 122 87
-55 88 89 122 123
-56 89 90 123 124
-57 90 91 124 125
-58 91 92 125 126
-59 92 93 126 127
-60 93 94 127 128
-61 94 95 128 129
-62 95 96 129 130
-63 96 97 130 131
-64 132 97 98 131
-65 99 132 133 98
-66 99 100 133 134
-67 100 101 134 135
-68 101 102 135 136
-69 1 2 3 4
-70 1 5 6 7
-71 5 8 9 10
-72 11 12 13 8
-73 11 14 15 16
-74 14 17 18 19
-75 22 17 20 21
-76 23 24 25 20
-77 23 26 27 28
-78 26 29 30 31
-79 33 34 29 32
-80 35 36 37 32
-81 35 38 39 40
-82 38 41 42 43
-83 44 45 46 41
-84 44 47 48 49
-85 2 47 50 51
-86 6 50 52 53
-87 3 52 9 54
-88 55 12 7 54
-89 55 56 15 10
-90 56 13 57 18
-91 57 58 16 21
-92 24 58 59 19
-93 22 59 27 60
-94 25 60 61 30
-95 33 28 61 62
-96 36 62 63 31
-97 34 39 63 64
-98 37 42 64 65
-99 66 45 40 65
-100 66 67 48 43
-101 67 46 68 51
-102 68 4 49 53
-103 1 2 3 4
-104 1 5 6 7
-105 5 8 9 10
-106 11 12 13 8
-107 11 14 15 16
-108 14 17 18 19
-109 22 17 20 21
-110 23 24 25 20
-111 23 26 27 28
-112 26 29 30 31
-113 33 34 29 32
-114 35 36 37 32
-115 35 38 39 40
-116 38 41 42 43
-117 44 45 46 41
-118 44 47 48 49
-119 2 47 50 51
-120 6 50 52 53
-121 3 52 9 54
-122 55 12 7 54
-123 55 56 15 10
-124 56 13 57 18
-125 57 58 16 21
-126 24 58 59 19
-127 22 59 27 60
-128 25 60 61 30
-129 33 28 61 62
-130 36 62 63 31
-131 34 39 63 64
-132 37 42 64 65
-133 66 45 40 65
-134 66 67 48 43
-135 67 46 68 51
-136 68 4 49 53
0

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