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On this page are computer-accessible forms for the graph C4[ 160, 68 ] = SDD(R_20(12,11)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {76, 108} under the group generated by the following permutations:

a: (14, 15)(17, 70)(18, 51)(19, 69)(20, 25)(21, 73)(22, 49)(44, 46)(47, 71)(48, 68)(50, 54)(52, 72)(86, 105)(87, 116)(96, 115)(97, 106)(126, 145)(127, 156)(136, 155)(137, 146)
b: (98, 138)
c: (113, 153)
d: (8, 9)(11, 45)(12, 66)(13, 65)(14, 44)(15, 46)(16, 41)(17, 49)(18, 47)(19, 48)(20, 25)(21, 73)(22, 70)(38, 40)(42, 64)(43, 67)(50, 54)(51, 71)(52, 72)(68, 69)(84, 103)(85, 95)(86, 96)(87, 116)(94, 113)(97, 106)(104, 114)(105, 115)(124, 143)(125, 135)(126, 136)(127, 156)(134, 153)(137, 146)(144, 154)(145, 155)
e: (109, 149)
f: (81, 121)
g: (17, 18)(20, 54)(21, 72)(22, 71)(23, 55)(24, 53)(25, 50)(26, 31)(27, 77)(28, 74)(47, 49)(51, 70)(52, 73)(56, 59)(57, 75)(58, 76)(87, 106)(88, 98)(89, 118)(97, 116)(99, 108)(107, 117)(127, 146)(128, 138)(129, 158)(137, 156)(139, 148)(147, 157)
h: (99, 139)
m: (105, 145)
n1: (84, 124)
a1: (110, 150)
b1: (106, 146)
c1: (103, 143)
d1: (112, 152)
e1: (108, 148)
f1: (86, 126)
g1: (1, 2, 56, 53, 50, 47, 44, 41, 38, 35, 32, 29, 26, 23, 20, 17, 14, 11, 8, 5)(3, 60, 58, 55, 52, 49, 46, 43, 40, 36, 33, 30, 27, 24, 21, 18, 15, 12, 9, 6)(4, 59, 57, 54, 51, 48, 45, 42, 39, 37, 34, 31, 28, 25, 22, 19, 16, 13, 10, 7)(61, 78, 76, 74, 72, 70, 68, 66, 64, 62, 80, 79, 77, 75, 73, 71, 69, 67, 65, 63)(81, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82)(101, 120, 119, 118, 117, 116, 115, 114, 113, 112, 111, 110, 109, 108, 107, 106, 105, 104, 103, 102)(121, 140, 139, 138, 137, 136, 135, 134, 133, 132, 131, 130, 129, 128, 127, 126, 125, 124, 123, 122)(141, 160, 159, 158, 157, 156, 155, 154, 153, 152, 151, 150, 149, 148, 147, 146, 145, 144, 143, 142)
h1: (97, 137)
m1: (100, 140)
n2: (118, 158)
a2: (104, 144)
b2: (89, 129)
c2: (119, 159)
d2: (101, 141)
e2: (111, 151)
f2: (2, 5)(3, 7)(4, 6)(8, 59)(9, 56)(10, 60)(11, 24)(12, 75)(13, 76)(14, 20)(15, 25)(16, 23)(18, 22)(19, 21)(26, 40)(27, 64)(28, 67)(29, 35)(30, 39)(31, 38)(33, 37)(34, 36)(41, 55)(42, 77)(43, 74)(44, 50)(45, 53)(46, 54)(48, 52)(49, 51)(57, 66)(58, 65)(62, 79)(63, 78)(68, 72)(69, 73)(81, 82)(83, 100)(84, 108)(85, 88)(86, 87)(89, 113)(90, 93)(91, 92)(94, 118)(95, 98)(96, 97)(99, 103)(101, 110)(102, 109)(104, 117)(105, 116)(106, 115)(107, 114)(111, 120)(112, 119)(121, 122)(123, 140)(124, 148)(125, 128)(126, 127)(129, 153)(130, 133)(131, 132)(134, 158)(135, 138)(136, 137)(139, 143)(141, 150)(142, 149)(144, 157)(145, 156)(146, 155)(147, 154)(151, 160)(152, 159)
g2: (102, 142)
h2: (95, 135)
m2: (115, 155)
n3: (11, 12)(14, 48)(15, 68)(16, 67)(17, 49)(18, 47)(19, 44)(20, 25)(21, 73)(22, 70)(41, 43)(45, 66)(46, 69)(50, 54)(51, 71)(52, 72)(85, 104)(86, 96)(87, 116)(95, 114)(97, 106)(105, 115)(125, 144)(126, 136)(127, 156)(135, 154)(137, 146)(145, 155)
a3: (91, 131)
b3: (120, 160)
c3: (107, 147)
d3: (92, 132)
e3: (83, 123)
f3: (116, 156)
g3: (82, 122)
h3: (20, 21)(23, 74)(24, 57)(25, 73)(26, 31)(27, 77)(28, 55)(50, 52)(53, 75)(54, 72)(56, 59)(58, 76)(88, 107)(89, 118)(98, 117)(99, 108)(128, 147)(129, 158)(138, 157)(139, 148)
m3: (87, 127)
n4: (114, 154)
a4: (94, 134)
b4: (5, 6)(8, 64)(9, 42)(10, 63)(11, 16)(12, 67)(13, 40)(35, 36)(38, 65)(39, 62)(41, 45)(43, 66)(83, 102)(84, 113)(93, 112)(94, 103)(123, 142)(124, 153)(133, 152)(134, 143)
c4: (117, 157)

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

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