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On this page are computer-accessible forms for the graph C4[ 160, 61 ] = SDD(C_40(1,9)).

(I) Following is a form readable by MAGMA:

g:=Graph<160|{ {78, 94}, {76, 93}, {74, 93}, {66, 90}, {74, 82}, {68, 92}, {67, 91}, {78, 85}, {77, 107}, {68, 110}, {73, 100}, {74, 101}, {80, 127}, {66, 112}, {76, 126}, {67, 117}, {73, 113}, {65, 120}, {74, 118}, {76, 114}, {64, 127}, {78, 113}, {29, 93}, {35, 99}, {59, 123}, {30, 95}, {41, 104}, {38, 103}, {32, 97}, {33, 99}, {48, 114}, {24, 91}, {40, 107}, {36, 103}, {23, 83}, {61, 121}, {60, 120}, {36, 96}, {25, 92}, {63, 122}, {35, 102}, {34, 100}, {42, 108}, {43, 109}, {44, 106}, {54, 112}, {33, 102}, {23, 94}, {54, 127}, {16, 90}, {17, 91}, {18, 89}, {53, 126}, {32, 108}, {49, 125}, {58, 118}, {59, 119}, {37, 104}, {62, 115}, {39, 106}, {57, 116}, {20, 90}, {61, 115}, {51, 125}, {19, 92}, {1, 81}, {37, 117}, {9, 89}, {42, 123}, {51, 98}, {1, 83}, {6, 84}, {50, 96}, {1, 82}, {34, 113}, {8, 91}, {2, 81}, {3, 87}, {49, 101}, {11, 94}, {47, 122}, {4, 82}, {15, 89}, {14, 88}, {10, 92}, {5, 83}, {1, 86}, {3, 84}, {2, 85}, {46, 121}, {58, 109}, {59, 108}, {4, 93}, {6, 95}, {2, 88}, {13, 87}, {12, 86}, {3, 89}, {52, 110}, {53, 111}, {5, 94}, {52, 111}, {32, 124}, {41, 117}, {7, 90}, {33, 124}, {9, 84}, {42, 119}, {43, 118}, {46, 115}, {9, 87}, {38, 120}, {11, 85}, {51, 109}, {35, 124}, {10, 106}, {23, 119}, {16, 112}, {4, 101}, {24, 121}, {8, 105}, {6, 103}, {2, 96}, {3, 97}, {5, 102}, {29, 126}, {28, 127}, {25, 122}, {50, 81}, {15, 107}, {17, 117}, {7, 98}, {27, 126}, {18, 116}, {48, 86}, {57, 95}, {50, 85}, {9, 97}, {18, 123}, {62, 87}, {21, 124}, {49, 88}, {30, 116}, {50, 88}, {8, 99}, {22, 125}, {14, 101}, {28, 112}, {7, 105}, {10, 100}, {7, 104}, {29, 114}, {10, 122}, {8, 121}, {24, 105}, {23, 102}, {4, 118}, {38, 84}, {5, 119}, {14, 125}, {25, 106}, {15, 123}, {27, 111}, {26, 110}, {22, 98}, {21, 97}, {26, 111}, {20, 98}, {31, 103}, {18, 107}, {38, 95}, {21, 108}, {11, 113}, {15, 116}, {24, 99}, {22, 109}, {45, 86}, {20, 104}, {45, 81}, {19, 110}, {25, 100}, {20, 105}, {6, 120}, {13, 115}, {12, 114}, {45, 83}, {31, 96}, {45, 82}, {30, 158}, {16, 148}, {28, 152}, {17, 149}, {19, 150}, {21, 147}, {29, 154}, {12, 132}, {12, 128}, {27, 151}, {14, 130}, {13, 129}, {31, 146}, {13, 130}, {30, 145}, {16, 131}, {26, 142}, {28, 136}, {17, 132}, {19, 133}, {11, 144}, {26, 134}, {60, 160}, {27, 135}, {22, 139}, {31, 129}, {41, 137}, {60, 156}, {56, 152}, {33, 128}, {39, 134}, {41, 136}, {47, 141}, {53, 151}, {55, 149}, {35, 128}, {47, 140}, {56, 155}, {40, 140}, {36, 129}, {46, 139}, {44, 138}, {56, 158}, {40, 143}, {42, 141}, {57, 158}, {43, 131}, {57, 145}, {44, 134}, {55, 157}, {37, 137}, {37, 136}, {39, 138}, {55, 154}, {58, 151}, {54, 152}, {61, 147}, {63, 144}, {34, 146}, {48, 128}, {40, 153}, {52, 134}, {63, 141}, {53, 135}, {32, 147}, {63, 140}, {49, 130}, {48, 132}, {44, 153}, {36, 146}, {61, 139}, {59, 141}, {56, 143}, {51, 139}, {55, 142}, {60, 133}, {58, 131}, {52, 142}, {43, 151}, {62, 130}, {46, 147}, {34, 156}, {39, 153}, {54, 136}, {47, 144}, {62, 129}, {71, 135}, {66, 131}, {80, 145}, {77, 140}, {68, 133}, {69, 135}, {77, 143}, {65, 133}, {75, 143}, {79, 138}, {72, 142}, {79, 137}, {67, 132}, {70, 138}, {70, 137}, {80, 159}, {75, 155}, {64, 145}, {71, 150}, {69, 148}, {68, 150}, {79, 157}, {72, 154}, {69, 150}, {75, 152}, {71, 148}, {77, 153}, {79, 155}, {72, 157}, {75, 158}, {73, 156}, {66, 148}, {76, 154}, {67, 149}, {71, 159}, {69, 159}, {70, 157}, {73, 146}, {65, 156}, {72, 149}, {70, 155}, {78, 144}, {64, 159}, {64, 160}, {65, 160}, {80, 160} }>;

(II) A more general form is to represent the graph as the orbit of {78, 94} under the group generated by the following permutations:

a: (47, 63)
b: (30, 57)
c: (29, 76)
d: (37, 41)
e: (5, 23)
f: (12, 48)
g: (8, 24)
h: (31, 36)
m: (3, 9)
n1: (22, 51)
a1: (42, 59)
b1: (39, 44)
c1: (17, 67)
d1: (7, 20)
e1: (27, 53)
f1: (55, 72)
g1: (6, 38)
h1: (11, 78)
m1: (21, 32)
n2: (64, 80)
a2: (14, 49)
b2: (2, 5)(4, 12)(6, 15)(8, 22)(13, 21)(14, 33)(16, 37)(17, 43)(18, 38)(19, 39)(23, 50)(24, 51)(27, 55)(31, 42)(32, 62)(34, 47)(35, 49)(36, 59)(40, 60)(41, 66)(44, 68)(48, 74)(53, 72)(56, 64)(58, 67)(63, 73)(65, 77)(69, 70)(71, 79)(75, 80)(81, 83)(82, 86)(84, 89)(85, 94)(87, 97)(88, 102)(90, 104)(91, 109)(92, 106)(93, 114)(95, 116)(96, 119)(98, 105)(99, 125)(100, 122)(101, 128)(103, 123)(107, 120)(108, 129)(110, 134)(111, 142)(112, 136)(113, 144)(115, 147)(117, 131)(118, 132)(121, 139)(124, 130)(126, 154)(127, 152)(133, 153)(135, 157)(137, 148)(138, 150)(140, 156)(141, 146)(143, 160)(145, 158)(149, 151)(155, 159)
c2: (28, 54)
d2: (16, 66)
e2: (60, 65)
f2: (33, 35)
g2: (26, 52)
h2: (1, 2)(3, 8)(4, 11)(5, 14)(6, 17)(7, 15)(9, 24)(10, 27)(12, 31)(13, 33)(16, 40)(18, 20)(19, 26)(21, 46)(22, 42)(23, 49)(25, 53)(28, 56)(29, 34)(30, 37)(32, 61)(35, 62)(36, 48)(38, 67)(39, 69)(41, 57)(43, 47)(44, 71)(45, 50)(51, 59)(52, 68)(54, 75)(55, 60)(58, 63)(64, 70)(65, 72)(66, 77)(73, 76)(74, 78)(79, 80)(82, 85)(83, 88)(84, 91)(86, 96)(87, 99)(89, 105)(90, 107)(92, 111)(93, 113)(94, 101)(95, 117)(97, 121)(98, 123)(100, 126)(102, 130)(103, 132)(104, 116)(106, 135)(108, 139)(109, 141)(112, 143)(114, 146)(115, 124)(118, 144)(119, 125)(120, 149)(122, 151)(127, 155)(128, 129)(131, 140)(133, 142)(134, 150)(136, 158)(137, 145)(138, 159)(148, 153)(154, 156)(157, 160)
m2: (2, 12)(3, 7)(4, 5)(6, 37)(8, 13)(9, 20)(10, 26)(11, 29)(14, 33)(15, 16)(17, 31)(18, 66)(19, 39)(21, 22)(23, 74)(24, 62)(25, 52)(27, 47)(28, 30)(32, 51)(34, 55)(35, 49)(36, 67)(38, 41)(40, 69)(42, 43)(44, 68)(48, 50)(53, 63)(54, 57)(56, 64)(58, 59)(60, 70)(65, 79)(71, 77)(72, 73)(75, 80)(76, 78)(81, 86)(82, 83)(84, 104)(85, 114)(87, 105)(88, 128)(89, 90)(91, 129)(92, 134)(93, 94)(95, 136)(96, 132)(97, 98)(99, 130)(100, 142)(101, 102)(103, 117)(106, 110)(107, 148)(108, 109)(111, 122)(112, 116)(113, 154)(115, 121)(118, 119)(120, 137)(123, 131)(124, 125)(126, 144)(127, 158)(133, 138)(135, 140)(139, 147)(141, 151)(143, 159)(145, 152)(146, 149)(150, 153)(155, 160)(156, 157)
n3: (13, 62)
a3: (43, 58)
b3: (46, 61)
c3: (10, 25)
d3: (15, 18)
e3: (2, 50)
f3: (34, 73)
g3: (69, 71)
h3: (70, 79)
m3: (4, 74)
n4: (19, 68)
a4: (56, 75)

(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[ 160, 61 ]
160
-1 81 82 83 86
-2 88 81 85 96
-3 89 84 97 87
-4 101 82 93 118
-5 102 83 94 119
-6 103 84 95 120
-7 90 104 105 98
-8 99 121 91 105
-9 89 84 97 87
-10 100 122 92 106
-11 144 113 94 85
-12 132 114 128 86
-13 115 129 130 87
-14 88 101 125 130
-15 89 123 116 107
-16 90 112 148 131
-17 132 91 149 117
-18 89 123 116 107
-19 110 133 92 150
-20 90 104 105 98
-21 124 147 97 108
-22 125 139 98 109
-23 102 83 94 119
-24 99 121 91 105
-25 100 122 92 106
-26 110 111 134 142
-27 111 135 126 151
-28 112 136 127 152
-29 154 114 93 126
-30 145 158 116 95
-31 146 103 96 129
-32 124 147 97 108
-33 99 102 124 128
-34 100 156 113 146
-35 99 102 124 128
-36 146 103 96 129
-37 136 104 137 117
-38 103 84 95 120
-39 134 138 106 153
-40 143 107 140 153
-41 136 104 137 117
-42 123 108 119 141
-43 118 151 109 131
-44 134 138 106 153
-45 81 82 83 86
-46 121 147 115 139
-47 122 144 140 141
-48 132 114 128 86
-49 88 101 125 130
-50 88 81 85 96
-51 125 139 98 109
-52 110 111 134 142
-53 111 135 126 151
-54 112 136 127 152
-55 154 157 149 142
-56 143 155 158 152
-57 145 158 116 95
-58 118 151 109 131
-59 123 108 119 141
-60 133 156 160 120
-61 121 147 115 139
-62 115 129 130 87
-63 122 144 140 141
-64 145 159 127 160
-65 133 156 160 120
-66 90 112 148 131
-67 132 91 149 117
-68 110 133 92 150
-69 135 148 159 150
-70 155 157 137 138
-71 135 148 159 150
-72 154 157 149 142
-73 100 156 113 146
-74 101 82 93 118
-75 143 155 158 152
-76 154 114 93 126
-77 143 107 140 153
-78 144 113 94 85
-79 155 157 137 138
-80 145 159 127 160
-81 1 45 2 50
-82 1 45 4 74
-83 1 23 45 5
-84 3 38 6 9
-85 11 78 2 50
-86 1 12 45 48
-87 13 3 62 9
-88 2 14 49 50
-89 3 15 18 9
-90 66 16 7 20
-91 67 24 17 8
-92 68 25 19 10
-93 4 29 74 76
-94 11 23 78 5
-95 57 38 6 30
-96 2 36 50 31
-97 3 9 21 32
-98 22 7 51 20
-99 33 24 35 8
-100 34 25 73 10
-101 14 4 49 74
-102 33 23 35 5
-103 36 38 6 31
-104 37 7 41 20
-105 24 7 8 20
-106 44 25 39 10
-107 77 15 18 40
-108 59 42 21 32
-109 22 58 51 43
-110 68 26 19 52
-111 26 27 52 53
-112 66 16 28 54
-113 11 34 78 73
-114 12 48 29 76
-115 13 46 61 62
-116 57 15 18 30
-117 67 37 17 41
-118 58 4 74 43
-119 23 59 5 42
-120 38 60 6 65
-121 24 46 61 8
-122 25 47 63 10
-123 15 59 18 42
-124 33 35 21 32
-125 22 14 49 51
-126 27 29 53 76
-127 80 28 64 54
-128 33 12 35 48
-129 13 36 62 31
-130 13 14 49 62
-131 66 58 16 43
-132 12 67 48 17
-133 68 60 19 65
-134 44 26 39 52
-135 69 27 71 53
-136 37 28 41 54
-137 79 37 70 41
-138 44 79 70 39
-139 22 46 61 51
-140 77 47 40 63
-141 47 59 63 42
-142 55 26 72 52
-143 77 56 40 75
-144 11 78 47 63
-145 57 80 30 64
-146 34 36 73 31
-147 46 61 21 32
-148 66 69 16 71
-149 55 67 17 72
-150 68 69 71 19
-151 58 27 53 43
-152 56 28 75 54
-153 44 77 39 40
-154 55 72 29 76
-155 56 79 70 75
-156 34 60 73 65
-157 55 79 70 72
-158 56 57 30 75
-159 69 80 71 64
-160 80 60 64 65
0

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