Graph forms
for C4 [ 192, 133 ] = SDD(MPS(4,24;5))
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On this page are computer-accessible forms for the graph C4[ 192, 133 ] =
SDD(MPS(4,24;5)).
(I) Following is a form readable by MAGMA:
g:=Graph<192|{ {66, 98}, {65, 99}, {75, 105}, {66, 103}, {66, 106}, {65, 104},
{65, 107}, {75, 97}, {66, 110}, {75, 102}, {65, 111}, {75, 100}, {84, 101}, {84,
97}, {84, 98}, {84, 99}, {41, 105}, {54, 119}, {55, 118}, {40, 106}, {42, 104},
{56, 124}, {57, 124}, {42, 108}, {53, 114}, {54, 113}, {55, 112}, {53, 120},
{56, 117}, {48, 126}, {55, 103}, {37, 119}, {40, 123}, {42, 121}, {41, 122},
{53, 102}, {54, 101}, {55, 100}, {56, 107}, {53, 109}, {43, 114}, {32, 122},
{41, 115}, {54, 108}, {35, 120}, {40, 116}, {45, 113}, {34, 127}, {48, 111}, {1,
97}, {29, 125}, {11, 107}, {10, 106}, {9, 105}, {8, 104}, {3, 98}, {20, 117},
{16, 113}, {14, 111}, {12, 109}, {7, 102}, {5, 100}, {1, 99}, {25, 123}, {24,
122}, {21, 119}, {20, 118}, {5, 103}, {1, 98}, {28, 127}, {23, 116}, {17, 114},
{13, 110}, {6, 101}, {2, 97}, {1, 101}, {31, 123}, {27, 127}, {8, 108}, {3,
103}, {2, 102}, {19, 118}, {2, 100}, {26, 124}, {19, 117}, {18, 116}, {4, 99},
{3, 106}, {6, 108}, {23, 125}, {20, 126}, {7, 109}, {2, 105}, {18, 121}, {4,
111}, {4, 104}, {28, 112}, {3, 110}, {30, 115}, {19, 126}, {22, 120}, {23, 121},
{4, 107}, {18, 125}, {13, 125}, {15, 127}, {14, 126}, {6, 119}, {10, 123}, {8,
121}, {5, 118}, {30, 109}, {29, 110}, {9, 122}, {5, 112}, {7, 114}, {6, 113},
{11, 124}, {9, 115}, {10, 116}, {11, 117}, {7, 120}, {15, 112}, {12, 115}, {16,
144}, {26, 154}, {25, 153}, {24, 152}, {17, 145}, {14, 143}, {22, 151}, {36,
160}, {22, 147}, {39, 162}, {14, 136}, {31, 153}, {15, 137}, {21, 146}, {38,
161}, {47, 167}, {8, 130}, {31, 149}, {13, 135}, {12, 134}, {9, 131}, {13, 129},
{26, 150}, {25, 149}, {24, 148}, {47, 163}, {44, 161}, {10, 132}, {12, 130},
{11, 133}, {46, 160}, {62, 176}, {63, 177}, {15, 128}, {16, 128}, {17, 129},
{22, 135}, {52, 166}, {82, 192}, {62, 172}, {63, 173}, {58, 169}, {59, 168},
{60, 175}, {26, 142}, {28, 137}, {27, 141}, {86, 192}, {50, 164}, {51, 165},
{27, 140}, {60, 171}, {20, 140}, {30, 134}, {16, 138}, {29, 135}, {25, 131},
{23, 141}, {17, 139}, {50, 168}, {51, 169}, {61, 167}, {21, 142}, {91, 192},
{21, 137}, {31, 131}, {30, 130}, {29, 129}, {28, 128}, {24, 132}, {27, 134},
{60, 161}, {52, 170}, {94, 192}, {61, 163}, {62, 160}, {18, 141}, {19, 140},
{58, 165}, {59, 164}, {43, 139}, {63, 159}, {50, 147}, {52, 150}, {44, 143},
{49, 146}, {57, 154}, {59, 152}, {63, 156}, {32, 132}, {35, 135}, {34, 134},
{33, 133}, {51, 151}, {61, 153}, {62, 155}, {44, 138}, {46, 136}, {60, 154},
{45, 138}, {51, 148}, {42, 130}, {59, 147}, {38, 143}, {52, 157}, {41, 131},
{43, 129}, {49, 155}, {50, 152}, {37, 142}, {36, 136}, {40, 132}, {39, 139},
{38, 138}, {37, 137}, {61, 145}, {45, 128}, {58, 151}, {34, 140}, {49, 159},
{58, 148}, {34, 141}, {57, 150}, {35, 147}, {44, 157}, {39, 149}, {46, 156},
{33, 146}, {32, 148}, {36, 144}, {35, 151}, {49, 133}, {47, 153}, {37, 146},
{57, 142}, {32, 152}, {36, 156}, {48, 136}, {39, 158}, {33, 155}, {43, 145},
{38, 157}, {45, 144}, {56, 133}, {33, 159}, {46, 144}, {47, 145}, {48, 143},
{67, 139}, {85, 158}, {76, 157}, {96, 178}, {67, 149}, {68, 156}, {96, 185},
{76, 150}, {68, 159}, {96, 188}, {67, 158}, {71, 154}, {64, 158}, {96, 190},
{69, 155}, {72, 168}, {95, 191}, {67, 162}, {92, 189}, {91, 186}, {90, 187},
{88, 185}, {81, 176}, {89, 187}, {90, 184}, {80, 179}, {70, 162}, {95, 187},
{94, 186}, {88, 188}, {64, 165}, {90, 191}, {83, 182}, {69, 160}, {79, 170},
{71, 161}, {88, 190}, {83, 181}, {76, 170}, {78, 168}, {74, 173}, {95, 184},
{93, 186}, {89, 190}, {87, 176}, {85, 178}, {80, 183}, {71, 175}, {89, 177},
{87, 191}, {68, 173}, {94, 183}, {92, 181}, {90, 179}, {69, 172}, {77, 164},
{76, 166}, {94, 180}, {92, 182}, {88, 178}, {77, 167}, {72, 163}, {93, 182},
{87, 188}, {86, 189}, {71, 171}, {95, 179}, {91, 183}, {74, 166}, {73, 164},
{81, 188}, {78, 163}, {64, 174}, {83, 189}, {81, 191}, {73, 167}, {70, 169},
{91, 180}, {82, 189}, {72, 184}, {93, 173}, {85, 165}, {73, 185}, {74, 186},
{70, 183}, {79, 190}, {64, 178}, {92, 174}, {80, 162}, {89, 170}, {77, 185},
{79, 187}, {68, 177}, {69, 176}, {70, 179}, {78, 184}, {77, 181}, {80, 169},
{86, 175}, {78, 180}, {86, 172}, {81, 171}, {85, 174}, {93, 166}, {72, 180},
{87, 171}, {73, 181}, {74, 182}, {82, 175}, {83, 174}, {79, 177}, {82, 172}
}>;
(II) A more general form is to represent the graph as the orbit of {66, 98}
under the group generated by the following permutations:
a: (7, 9)(10, 13)(17, 24)(22, 25)(29, 40)(31, 35)(32, 43)(39, 51)(41, 53)(47,
50)(58, 67)(59, 61)(102, 105)(106, 110)(109, 115)(114, 122)(116, 125)(120,
131)(123, 135)(129, 132)(139, 148)(145, 152)(147, 153)(149, 151)(158, 165)(162,
169)(163, 168)(164, 167) (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 **************
b: (73, 77)
c: (1, 2)(3, 5)(4, 7)(6, 9)(8, 12)(10, 15)(11, 17)(13, 19)(14, 22)(16, 24)(18,
27)(20, 29)(21, 25)(23, 34)(26, 39)(28, 40)(30, 42)(31, 37)(32, 45)(33, 47)(35,
48)(36, 50)(38, 51)(41, 54)(43, 56)(44, 58)(46, 59)(49, 61)(52, 64)(53, 65)(55,
66)(57, 67)(60, 70)(62, 72)(63, 73)(68, 77)(69, 78)(71, 80)(74, 83)(75, 84)(76,
85)(79, 88)(81, 90)(82, 91)(86, 94)(87, 95)(89, 96)(92, 93)(98, 100)(99,
102)(101, 105)(104, 109)(106, 112)(107, 114)(108, 115)(110, 118)(111, 120)(113,
122)(116, 127)(117, 129)(119, 131)(121, 134)(123, 137)(124, 139)(125, 140)(126,
135)(128, 132)(133, 145)(136, 147)(138, 148)(142, 149)(143, 151)(144, 152)(146,
153)(150, 158)(154, 162)(155, 163)(156, 164)(157, 165)(159, 167)(160, 168)(161,
169)(166, 174)(170, 178)(171, 179)(172, 180)(173, 181)(175, 183)(176, 184)(177,
185)(186, 189)(187, 188)
d: (7, 53)
e: (33, 49)
f: (74, 93)
g: (26, 57)
h: (39, 67)
m: (22, 35)
n1: (4, 65)
a1: (3, 66)
b1: (91, 94)
c1: (83, 92)
d1: (62, 69)
e1: (72, 78)
f1: (26, 33)(36, 38)(44, 46)(49, 57)(52, 63)(60, 62)(68, 76)(69, 71)(124,
133)(136, 143)(138, 144)(142, 146)(150, 159)(154, 155)(156, 157)(160, 161)(166,
173)(170, 177)(171, 176)(172, 175)
g1: (21, 37)
h1: (60, 71)
m1: (15, 28)
n2: (11, 14)(16, 21)(26, 38)(33, 36)(37, 45)(44, 57)(46, 49)(48, 56)(107,
111)(113, 119)(117, 126)(124, 143)(128, 137)(133, 136)(138, 142)(144, 146)(150,
157)(154, 161)(155, 160)(156, 159)
a2: (50, 59)
b2: (2, 75)
c2: (10, 40)
d2: (38, 44)
e2: (51, 58)
f2: (63, 68)
g2: (74, 79)(81, 82)(83, 88)(86, 87)(89, 93)(90, 91)(92, 96)(94, 95)(166,
170)(171, 175)(172, 176)(173, 177)(174, 178)(179, 183)(180, 184)(181, 185)(182,
190)(186, 187)(188, 189)(191, 192)
h2: (52, 60)(62, 63)(68, 69)(71, 76)(74, 82)(79, 81)(86, 93)(87, 89)(150,
154)(155, 159)(156, 160)(157, 161)(166, 175)(170, 171)(172, 173)(176, 177)(182,
189)(186, 192)(187, 191)(188, 190)
m2: (88, 96)
n3: (13, 29)
a3: (4, 6)(11, 16)(14, 21)(15, 19)(20, 28)(26, 38)(33, 36)(37, 48)(44, 57)(45,
56)(46, 49)(54, 65)(99, 101)(104, 108)(107, 113)(111, 119)(112, 118)(117,
128)(124, 138)(126, 137)(127, 140)(133, 144)(136, 146)(142, 143)(150, 157)(154,
161)(155, 160)(156, 159)
b3: (6, 54)
c3: (25, 31)
d3: (16, 45)
e3: (64, 70)(72, 73)(74, 79)(77, 78)(80, 85)(81, 82)(83, 90)(86, 87)(88, 91)(89,
93)(92, 95)(94, 96)(158, 162)(163, 167)(164, 168)(165, 169)(166, 170)(171,
175)(172, 176)(173, 177)(174, 179)(178, 183)(180, 185)(181, 184)(182, 187)(186,
190)(188, 192)(189, 191)
f3: (5, 55)
g3: (82, 86)
h3: (70, 80)
m3: (2, 6, 3, 4)(5, 8)(7, 21, 13, 11)(9, 16, 10, 14)(12, 15, 18, 19)(17, 26)(20,
30, 28, 23)(22, 33)(24, 36)(25, 38)(29, 56, 53, 37)(31, 44)(32, 46)(35, 49)(39,
52)(40, 48, 41, 45)(42, 55)(43, 57)(47, 60)(50, 62)(51, 63)(54, 66, 65, 75)(58,
68)(59, 69)(61, 71)(64, 74, 70, 79)(67, 76)(72, 81, 73, 82)(77, 86, 78, 87)(80,
89, 85, 93)(83, 91, 90, 88)(92, 94, 95, 96)(97, 101, 98, 99)(100, 108, 103,
104)(102, 119, 110, 107)(105, 113, 106, 111)(109, 137, 125, 117)(112, 121, 118,
130)(114, 142, 129, 124)(115, 128, 116, 126)(120, 146, 135, 133)(122, 144, 132,
136)(123, 143, 131, 138)(127, 141, 140, 134)(139, 150)(145, 154)(147, 155)(148,
156)(149, 157)(151, 159)(152, 160)(153, 161)(158, 166, 162, 170)(163, 171, 167,
175)(164, 172, 168, 176)(165, 173, 169, 177)(174, 186, 179, 190)(178, 182, 183,
187)(180, 191, 185, 189)(181, 192, 184, 188)
n4: (27, 34)
a4: (36, 46)
b4: (19, 20)
c4: (47, 61)
d4: (14, 48)
e4: (8, 42)
f4: (81, 87)
g4: (39, 47)(50, 51)(58, 59)(61, 67)(64, 72)(70, 73)(74, 79)(77, 80)(78, 85)(81,
82)(83, 90)(86, 87)(88, 91)(89, 93)(92, 95)(94, 96)(139, 145)(147, 151)(148,
152)(149, 153)(158, 163)(162, 167)(164, 169)(165, 168)(166, 170)(171, 175)(172,
176)(173, 177)(174, 184)(178, 180)(179, 181)(182, 187)(183, 185)(186, 190)(188,
192)(189, 191)
h4: (9, 41)
m4: (24, 32)
n5: (17, 22)(24, 25)(31, 32)(35, 43)(39, 51)(47, 50)(58, 67)(59, 61)(114,
120)(122, 131)(123, 132)(129, 135)(139, 151)(145, 147)(148, 149)(152, 153)(158,
165)(162, 169)(163, 168)(164, 167)
a5: (18, 23)
C4[ 192, 133 ]
192
-1 99 101 97 98
-2 100 102 105 97
-3 110 103 106 98
-4 99 111 104 107
-5 100 112 103 118
-6 101 113 108 119
-7 102 114 109 120
-8 121 104 108 130
-9 122 115 105 131
-10 132 123 116 106
-11 133 124 117 107
-12 134 115 130 109
-13 110 135 125 129
-14 143 111 136 126
-15 112 137 127 128
-16 144 113 138 128
-17 145 114 139 129
-18 121 125 116 141
-19 126 117 118 140
-20 126 117 118 140
-21 146 137 119 142
-22 135 147 151 120
-23 121 125 116 141
-24 132 122 148 152
-25 123 149 131 153
-26 154 124 150 142
-27 134 127 140 141
-28 112 137 127 128
-29 110 135 125 129
-30 134 115 130 109
-31 123 149 131 153
-32 132 122 148 152
-33 133 155 146 159
-34 134 127 140 141
-35 135 147 151 120
-36 144 156 136 160
-37 146 137 119 142
-38 143 157 138 161
-39 158 149 139 162
-40 132 123 116 106
-41 122 115 105 131
-42 121 104 108 130
-43 145 114 139 129
-44 143 157 138 161
-45 144 113 138 128
-46 144 156 136 160
-47 145 167 163 153
-48 143 111 136 126
-49 133 155 146 159
-50 168 147 152 164
-51 165 169 148 151
-52 166 157 170 150
-53 102 114 109 120
-54 101 113 108 119
-55 100 112 103 118
-56 133 124 117 107
-57 154 124 150 142
-58 165 169 148 151
-59 168 147 152 164
-60 154 171 161 175
-61 145 167 163 153
-62 176 155 160 172
-63 177 156 159 173
-64 165 178 158 174
-65 99 111 104 107
-66 110 103 106 98
-67 158 149 139 162
-68 177 156 159 173
-69 176 155 160 172
-70 179 169 183 162
-71 154 171 161 175
-72 168 180 184 163
-73 167 181 185 164
-74 166 182 173 186
-75 100 102 105 97
-76 166 157 170 150
-77 167 181 185 164
-78 168 180 184 163
-79 187 177 190 170
-80 179 169 183 162
-81 176 188 191 171
-82 189 192 172 175
-83 189 181 182 174
-84 99 101 97 98
-85 165 178 158 174
-86 189 192 172 175
-87 176 188 191 171
-88 188 178 190 185
-89 187 177 190 170
-90 187 179 191 184
-91 180 192 183 186
-92 189 181 182 174
-93 166 182 173 186
-94 180 192 183 186
-95 187 179 191 184
-96 188 178 190 185
-97 1 2 84 75
-98 66 1 3 84
-99 1 4 84 65
-100 55 2 5 75
-101 1 6 84 54
-102 2 7 53 75
-103 55 66 3 5
-104 4 8 42 65
-105 2 41 9 75
-106 66 3 40 10
-107 11 56 4 65
-108 6 8 42 54
-109 12 7 30 53
-110 66 13 3 29
-111 14 4 48 65
-112 55 15 5 28
-113 45 16 6 54
-114 17 7 53 43
-115 12 30 41 9
-116 23 18 40 10
-117 11 56 19 20
-118 55 5 19 20
-119 37 6 21 54
-120 22 35 7 53
-121 23 18 8 42
-122 24 41 9 32
-123 25 40 31 10
-124 11 56 57 26
-125 23 13 18 29
-126 14 48 19 20
-127 34 15 27 28
-128 45 15 16 28
-129 13 17 29 43
-130 12 8 30 42
-131 25 41 9 31
-132 24 40 10 32
-133 11 33 56 49
-134 12 34 27 30
-135 22 13 35 29
-136 46 14 36 48
-137 15 37 28 21
-138 44 45 16 38
-139 67 17 39 43
-140 34 27 19 20
-141 23 34 27 18
-142 57 26 37 21
-143 44 14 48 38
-144 45 46 36 16
-145 47 17 61 43
-146 33 37 49 21
-147 22 35 59 50
-148 24 58 51 32
-149 67 25 39 31
-150 57 26 52 76
-151 22 35 58 51
-152 24 59 50 32
-153 25 47 61 31
-154 57 26 60 71
-155 33 69 49 62
-156 46 68 36 63
-157 44 38 52 76
-158 67 39 85 64
-159 33 68 49 63
-160 46 36 69 62
-161 44 38 60 71
-162 67 80 70 39
-163 78 47 61 72
-164 77 59 50 73
-165 58 51 85 64
-166 93 52 74 76
-167 77 47 61 73
-168 78 59 50 72
-169 58 80 70 51
-170 89 79 52 76
-171 81 60 71 87
-172 69 82 62 86
-173 68 93 63 74
-174 92 83 85 64
-175 60 71 82 86
-176 69 81 62 87
-177 89 68 79 63
-178 88 85 96 64
-179 90 80 70 95
-180 78 91 72 94
-181 77 92 83 73
-182 92 93 83 74
-183 80 91 70 94
-184 78 90 72 95
-185 77 88 73 96
-186 91 93 94 74
-187 89 79 90 95
-188 88 81 96 87
-189 92 82 83 86
-190 88 89 79 96
-191 90 81 95 87
-192 91 82 94 86
0