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On this page are computer-accessible forms for the graph C4[ 140, 9 ] = SDD(C_35(1,6)).

(I) Following is a form readable by MAGMA:

g:=Graph<140|{ {67, 71}, {66, 74}, {67, 75}, {68, 77}, {67, 73}, {68, 78}, {67, 72}, {66, 82}, {66, 83}, {66, 87}, {65, 90}, {65, 92}, {68, 90}, {68, 91}, {70, 101}, {70, 99}, {69, 111}, {65, 111}, {65, 113}, {69, 112}, {70, 126}, {70, 124}, {64, 124}, {64, 125}, {48, 114}, {33, 98}, {45, 105}, {48, 116}, {50, 118}, {2, 71}, {59, 126}, {8, 77}, {46, 107}, {47, 106}, {54, 115}, {1, 71}, {9, 79}, {8, 78}, {41, 110}, {54, 113}, {1, 73}, {58, 114}, {2, 74}, {53, 125}, {1, 72}, {18, 91}, {16, 89}, {1, 75}, {58, 112}, {4, 78}, {43, 97}, {53, 127}, {3, 72}, {17, 90}, {7, 76}, {19, 95}, {2, 79}, {17, 92}, {6, 75}, {4, 73}, {37, 104}, {45, 96}, {47, 98}, {2, 76}, {35, 109}, {3, 77}, {41, 103}, {5, 74}, {18, 93}, {36, 107}, {60, 108}, {43, 122}, {53, 100}, {4, 86}, {32, 114}, {8, 90}, {5, 87}, {36, 118}, {53, 103}, {3, 80}, {13, 94}, {8, 91}, {7, 84}, {51, 96}, {32, 116}, {44, 120}, {45, 121}, {50, 102}, {4, 81}, {33, 116}, {6, 83}, {42, 127}, {3, 85}, {55, 97}, {33, 119}, {11, 93}, {10, 92}, {5, 83}, {5, 82}, {15, 88}, {40, 127}, {6, 94}, {12, 84}, {7, 95}, {43, 115}, {14, 87}, {60, 101}, {39, 126}, {10, 80}, {60, 102}, {35, 121}, {34, 120}, {33, 123}, {11, 81}, {38, 124}, {13, 86}, {63, 100}, {38, 125}, {46, 117}, {51, 104}, {9, 85}, {63, 99}, {37, 120}, {49, 108}, {6, 88}, {55, 105}, {12, 82}, {7, 89}, {36, 122}, {37, 123}, {41, 119}, {50, 109}, {17, 113}, {56, 88}, {26, 122}, {18, 114}, {52, 84}, {9, 104}, {58, 91}, {22, 119}, {11, 106}, {14, 108}, {22, 116}, {18, 112}, {15, 109}, {10, 105}, {24, 125}, {28, 121}, {13, 107}, {56, 94}, {21, 115}, {51, 85}, {16, 119}, {58, 93}, {24, 127}, {55, 80}, {12, 100}, {61, 85}, {57, 81}, {29, 117}, {19, 123}, {14, 102}, {9, 96}, {23, 126}, {15, 102}, {11, 98}, {50, 88}, {10, 97}, {63, 84}, {60, 87}, {56, 83}, {23, 124}, {19, 120}, {14, 101}, {52, 95}, {55, 92}, {25, 117}, {31, 115}, {26, 118}, {20, 121}, {63, 82}, {61, 80}, {22, 123}, {52, 89}, {30, 112}, {31, 113}, {12, 99}, {57, 86}, {21, 122}, {41, 89}, {61, 77}, {57, 73}, {46, 94}, {26, 107}, {62, 79}, {30, 111}, {28, 109}, {23, 101}, {62, 76}, {47, 93}, {25, 106}, {56, 75}, {29, 110}, {20, 96}, {62, 74}, {23, 99}, {22, 98}, {21, 97}, {61, 72}, {16, 103}, {57, 78}, {29, 106}, {27, 108}, {25, 110}, {13, 117}, {46, 86}, {52, 76}, {15, 118}, {62, 71}, {37, 95}, {19, 104}, {24, 100}, {51, 79}, {20, 105}, {16, 110}, {17, 111}, {47, 81}, {24, 103}, {21, 132}, {31, 138}, {26, 140}, {20, 131}, {31, 136}, {28, 132}, {30, 134}, {30, 135}, {27, 129}, {25, 130}, {27, 128}, {28, 129}, {27, 133}, {29, 130}, {38, 134}, {39, 135}, {42, 138}, {34, 131}, {35, 129}, {40, 138}, {40, 140}, {42, 140}, {34, 133}, {35, 132}, {39, 128}, {44, 139}, {36, 140}, {42, 130}, {32, 137}, {34, 139}, {44, 133}, {40, 130}, {32, 139}, {38, 136}, {39, 137}, {45, 131}, {43, 132}, {44, 131}, {49, 129}, {49, 128}, {59, 137}, {49, 133}, {48, 137}, {48, 139}, {59, 128}, {54, 138}, {59, 135}, {54, 136}, {69, 135}, {69, 134}, {64, 134}, {64, 136} }>;

(II) A more general form is to represent the graph as the orbit of {67, 71} under the group generated by the following permutations:

a: (30, 69)
b: (1, 2)(3, 5)(4, 7)(6, 9)(8, 12)(10, 14)(11, 16)(13, 19)(15, 20)(17, 23)(18, 24)(21, 27)(22, 25)(26, 34)(29, 33)(30, 38)(31, 39)(32, 40)(36, 44)(37, 46)(41, 47)(42, 48)(43, 49)(45, 50)(51, 56)(52, 57)(53, 58)(54, 59)(55, 60)(61, 66)(62, 67)(63, 68)(64, 69)(65, 70)(72, 74)(73, 76)(75, 79)(77, 82)(78, 84)(80, 87)(81, 89)(83, 85)(86, 95)(88, 96)(90, 99)(91, 100)(92, 101)(93, 103)(94, 104)(97, 108)(98, 110)(102, 105)(106, 119)(107, 120)(109, 121)(111, 124)(112, 125)(113, 126)(114, 127)(115, 128)(116, 130)(117, 123)(118, 131)(122, 133)(129, 132)(135, 136)(137, 138)(139, 140)
c: (40, 42)
d: (34, 44)
e: (39, 59)
f: (2, 62)
g: (7, 52)
h: (15, 50)
m: (32, 48)
n1: (22, 33)
a1: (4, 57)
b1: (38, 64)
c1: (9, 51)
d1: (5, 66)
e1: (14, 60)
f1: (10, 55)
g1: (2, 6)(3, 4)(7, 15)(9, 13)(10, 11)(12, 14)(16, 28)(17, 18)(19, 26)(20, 25)(21, 22)(24, 27)(29, 45)(31, 32)(33, 43)(34, 40)(35, 41)(36, 37)(38, 39)(42, 44)(46, 51)(47, 55)(48, 54)(49, 53)(50, 52)(56, 62)(57, 61)(58, 65)(59, 64)(60, 63)(71, 75)(72, 73)(74, 83)(76, 88)(77, 78)(79, 94)(80, 81)(82, 87)(84, 102)(85, 86)(89, 109)(90, 91)(92, 93)(95, 118)(96, 117)(97, 98)(99, 101)(100, 108)(103, 129)(104, 107)(105, 106)(110, 121)(111, 112)(113, 114)(115, 116)(119, 132)(120, 140)(122, 123)(124, 126)(125, 128)(127, 133)(130, 131)(134, 135)(136, 137)(138, 139)
h1: (18, 58)
m1: (23, 70)
n2: (12, 63)
a2: (31, 54)
b2: (2, 3)(4, 6)(5, 8)(7, 10)(11, 15)(12, 17)(14, 18)(16, 21)(19, 20)(22, 28)(23, 30)(24, 31)(25, 26)(27, 32)(29, 36)(33, 35)(37, 45)(41, 43)(47, 50)(48, 49)(52, 55)(53, 54)(56, 57)(58, 60)(61, 62)(63, 65)(66, 68)(69, 70)(71, 72)(73, 75)(74, 77)(76, 80)(78, 83)(79, 85)(81, 88)(82, 90)(84, 92)(86, 94)(87, 91)(89, 97)(93, 102)(95, 105)(96, 104)(98, 109)(99, 111)(100, 113)(101, 112)(103, 115)(106, 118)(107, 117)(108, 114)(110, 122)(116, 129)(119, 132)(120, 131)(121, 123)(124, 134)(125, 136)(126, 135)(127, 138)(128, 137)(130, 140)(133, 139)
c2: (13, 46)
d2: (20, 45)
e2: (6, 56)
f2: (25, 29)
g2: (28, 35)
h2: (16, 41)
m2: (11, 47)
n3: (3, 61)
a3: (19, 37)
b3: (17, 65)
c3: (21, 43)
d3: (8, 68)
e3: (26, 36)
f3: (27, 49)

(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[ 140, 9 ]
140
-1 71 72 73 75
-2 79 71 74 76
-3 77 80 72 85
-4 78 81 73 86
-5 82 83 74 87
-6 88 83 94 75
-7 89 84 95 76
-8 77 78 90 91
-9 79 104 85 96
-10 80 92 105 97
-11 81 93 106 98
-12 99 100 82 84
-13 94 117 107 86
-14 101 102 108 87
-15 88 102 118 109
-16 110 89 103 119
-17 111 90 113 92
-18 112 91 114 93
-19 123 104 95 120
-20 121 105 96 131
-21 132 122 115 97
-22 123 116 119 98
-23 99 101 124 126
-24 100 103 125 127
-25 110 106 117 130
-26 122 107 118 140
-27 133 128 129 108
-28 121 132 129 109
-29 110 106 117 130
-30 111 112 134 135
-31 113 136 115 138
-32 114 137 116 139
-33 123 116 119 98
-34 133 139 120 131
-35 121 132 129 109
-36 122 107 118 140
-37 123 104 95 120
-38 134 124 125 136
-39 135 126 137 128
-40 127 138 140 130
-41 110 89 103 119
-42 127 138 140 130
-43 132 122 115 97
-44 133 139 120 131
-45 121 105 96 131
-46 94 117 107 86
-47 81 93 106 98
-48 114 137 116 139
-49 133 128 129 108
-50 88 102 118 109
-51 79 104 85 96
-52 89 84 95 76
-53 100 103 125 127
-54 113 136 115 138
-55 80 92 105 97
-56 88 83 94 75
-57 78 81 73 86
-58 112 91 114 93
-59 135 126 137 128
-60 101 102 108 87
-61 77 80 72 85
-62 79 71 74 76
-63 99 100 82 84
-64 134 124 125 136
-65 111 90 113 92
-66 82 83 74 87
-67 71 72 73 75
-68 77 78 90 91
-69 111 112 134 135
-70 99 101 124 126
-71 1 67 2 62
-72 1 67 3 61
-73 1 67 57 4
-74 66 2 5 62
-75 1 56 67 6
-76 2 7 62 52
-77 68 3 61 8
-78 57 68 4 8
-79 2 51 62 9
-80 55 3 61 10
-81 11 57 47 4
-82 66 12 5 63
-83 66 56 5 6
-84 12 7 52 63
-85 3 61 51 9
-86 13 46 57 4
-87 66 14 5 60
-88 56 15 6 50
-89 16 7 41 52
-90 68 17 8 65
-91 68 58 18 8
-92 55 17 10 65
-93 11 47 58 18
-94 56 13 46 6
-95 37 7 19 52
-96 45 51 9 20
-97 55 10 21 43
-98 11 22 33 47
-99 12 23 70 63
-100 12 24 63 53
-101 23 14 70 60
-102 14 15 60 50
-103 24 16 41 53
-104 37 51 19 9
-105 55 45 20 10
-106 11 25 47 29
-107 13 46 36 26
-108 14 27 49 60
-109 35 15 28 50
-110 25 16 29 41
-111 69 17 30 65
-112 58 69 18 30
-113 17 31 54 65
-114 58 48 18 32
-115 31 21 43 54
-116 22 33 48 32
-117 13 46 25 29
-118 36 15 26 50
-119 22 33 16 41
-120 44 34 37 19
-121 45 35 28 20
-122 36 26 21 43
-123 22 33 37 19
-124 23 70 38 64
-125 24 38 53 64
-126 23 59 70 39
-127 24 40 42 53
-128 59 27 49 39
-129 35 27 49 28
-130 25 29 40 42
-131 44 34 45 20
-132 35 28 21 43
-133 44 34 27 49
-134 69 38 30 64
-135 69 59 39 30
-136 38 31 64 54
-137 48 59 39 32
-138 40 31 42 54
-139 44 34 48 32
-140 36 26 40 42
0

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