[Home] [Table] [Glossary] [Families]

On this page are computer-accessible forms for the graph C4[ 216, 79 ] = SDD(W(27,2)).

(I) Following is a form readable by MAGMA:

g:=Graph<216|{ {66, 119}, {70, 115}, {75, 126}, {70, 125}, {66, 126}, {66, 127}, {60, 124}, {54, 119}, {44, 110}, {57, 123}, {57, 113}, {60, 117}, {60, 112}, {62, 114}, {57, 116}, {60, 115}, {62, 110}, {62, 111}, {35, 112}, {43, 120}, {62, 109}, {43, 127}, {57, 109}, {35, 118}, {44, 121}, {33, 118}, {42, 114}, {45, 116}, {33, 125}, {40, 117}, {28, 124}, {25, 123}, {30, 122}, {24, 126}, {22, 113}, {16, 120}, {20, 124}, {17, 120}, {4, 110}, {5, 111}, {1, 109}, {23, 123}, {22, 122}, {1, 111}, {1, 110}, {22, 121}, {2, 109}, {3, 115}, {10, 122}, {6, 118}, {7, 118}, {30, 111}, {12, 125}, {9, 120}, {1, 114}, {10, 121}, {3, 112}, {2, 113}, {2, 116}, {9, 127}, {8, 126}, {6, 112}, {3, 117}, {8, 127}, {15, 119}, {2, 123}, {13, 116}, {11, 114}, {7, 125}, {10, 113}, {14, 117}, {4, 121}, {3, 124}, {12, 115}, {8, 119}, {5, 122}, {11, 139}, {81, 209}, {80, 208}, {19, 147}, {17, 145}, {10, 139}, {83, 210}, {78, 207}, {21, 148}, {16, 145}, {13, 140}, {76, 205}, {69, 199}, {90, 216}, {81, 211}, {79, 205}, {74, 200}, {14, 141}, {87, 212}, {77, 206}, {55, 180}, {4, 128}, {85, 209}, {37, 161}, {12, 136}, {7, 131}, {6, 130}, {5, 129}, {76, 200}, {77, 201}, {73, 204}, {93, 216}, {87, 210}, {38, 160}, {85, 211}, {39, 161}, {48, 182}, {49, 183}, {19, 148}, {83, 212}, {38, 161}, {28, 155}, {24, 159}, {72, 207}, {74, 205}, {4, 140}, {95, 215}, {93, 213}, {45, 165}, {6, 143}, {95, 214}, {42, 163}, {37, 172}, {24, 145}, {21, 156}, {19, 154}, {15, 134}, {69, 204}, {7, 141}, {5, 142}, {39, 172}, {34, 169}, {18, 153}, {8, 132}, {79, 195}, {9, 133}, {55, 187}, {36, 169}, {38, 171}, {48, 189}, {50, 191}, {40, 166}, {94, 208}, {59, 181}, {73, 199}, {20, 155}, {90, 213}, {79, 192}, {49, 190}, {30, 142}, {46, 191}, {91, 202}, {80, 193}, {54, 167}, {41, 187}, {47, 189}, {27, 136}, {32, 179}, {92, 200}, {18, 135}, {16, 134}, {18, 132}, {17, 135}, {15, 152}, {31, 136}, {23, 128}, {20, 131}, {17, 134}, {16, 135}, {29, 133}, {82, 202}, {49, 169}, {72, 208}, {9, 144}, {92, 197}, {86, 207}, {27, 130}, {25, 128}, {14, 151}, {47, 182}, {61, 164}, {19, 137}, {91, 193}, {32, 186}, {13, 150}, {26, 129}, {59, 160}, {86, 202}, {22, 139}, {82, 207}, {41, 180}, {31, 130}, {51, 174}, {11, 149}, {78, 208}, {12, 146}, {21, 138}, {94, 193}, {30, 129}, {28, 131}, {44, 140}, {107, 203}, {105, 201}, {103, 199}, {102, 198}, {100, 196}, {99, 195}, {98, 194}, {46, 142}, {47, 143}, {35, 130}, {104, 201}, {45, 140}, {42, 139}, {26, 184}, {108, 206}, {33, 131}, {48, 146}, {49, 147}, {58, 152}, {52, 151}, {103, 196}, {101, 198}, {100, 199}, {99, 192}, {56, 155}, {29, 185}, {97, 197}, {61, 153}, {40, 141}, {107, 206}, {51, 150}, {58, 159}, {63, 154}, {104, 206}, {106, 204}, {50, 149}, {108, 203}, {55, 144}, {11, 163}, {106, 194}, {34, 138}, {15, 167}, {14, 166}, {13, 165}, {27, 178}, {97, 200}, {32, 137}, {53, 159}, {27, 176}, {63, 148}, {29, 177}, {101, 201}, {44, 128}, {35, 143}, {33, 141}, {63, 147}, {31, 178}, {102, 203}, {53, 152}, {36, 138}, {99, 205}, {98, 204}, {43, 133}, {54, 152}, {55, 153}, {31, 176}, {105, 198}, {52, 155}, {56, 151}, {41, 153}, {100, 212}, {98, 210}, {54, 134}, {103, 214}, {105, 216}, {24, 170}, {100, 214}, {103, 212}, {25, 173}, {101, 209}, {28, 168}, {26, 175}, {98, 215}, {18, 164}, {96, 214}, {63, 137}, {21, 162}, {96, 215}, {25, 174}, {105, 209}, {107, 211}, {106, 210}, {23, 174}, {108, 213}, {41, 144}, {39, 158}, {36, 157}, {29, 164}, {26, 163}, {61, 132}, {23, 173}, {38, 156}, {36, 158}, {61, 135}, {37, 158}, {45, 150}, {43, 144}, {46, 149}, {20, 168}, {34, 158}, {50, 142}, {32, 157}, {106, 215}, {101, 216}, {39, 154}, {47, 146}, {107, 213}, {34, 157}, {108, 211}, {42, 149}, {40, 151}, {37, 154}, {48, 143}, {68, 133}, {104, 171}, {88, 156}, {66, 132}, {102, 160}, {71, 129}, {84, 157}, {89, 147}, {65, 138}, {99, 175}, {91, 150}, {70, 136}, {102, 181}, {70, 146}, {104, 188}, {75, 159}, {65, 148}, {97, 184}, {75, 145}, {96, 186}, {65, 156}, {84, 137}, {96, 190}, {97, 191}, {68, 164}, {87, 183}, {86, 182}, {83, 179}, {82, 178}, {81, 177}, {80, 176}, {79, 175}, {74, 170}, {67, 162}, {95, 190}, {90, 187}, {85, 180}, {73, 168}, {75, 170}, {64, 162}, {65, 162}, {94, 189}, {92, 191}, {90, 185}, {78, 173}, {69, 166}, {71, 163}, {93, 185}, {92, 184}, {87, 179}, {86, 178}, {85, 177}, {83, 183}, {82, 182}, {72, 173}, {95, 186}, {81, 180}, {76, 170}, {93, 187}, {77, 171}, {84, 179}, {89, 190}, {71, 175}, {76, 167}, {78, 165}, {64, 172}, {69, 168}, {80, 189}, {72, 165}, {74, 167}, {46, 192}, {94, 176}, {89, 183}, {84, 186}, {67, 172}, {73, 166}, {52, 196}, {89, 169}, {53, 197}, {59, 203}, {77, 188}, {50, 192}, {51, 193}, {88, 171}, {64, 181}, {91, 174}, {68, 177}, {52, 194}, {53, 195}, {67, 181}, {88, 160}, {51, 202}, {88, 161}, {58, 195}, {56, 194}, {56, 196}, {64, 188}, {59, 198}, {68, 185}, {58, 197}, {67, 188}, {71, 184} }>;

(II) A more general form is to represent the graph as the orbit of {66, 119} under the group generated by the following permutations:

a: (4, 44)
b: (37, 39)
c: (81, 85)
d: (9, 18)(43, 61)(120, 135)(127, 132)(133, 164)(144, 153)
e: (10, 22)
f: (1, 2)(3, 8)(4, 10)(5, 13)(6, 15)(7, 16)(9, 14)(11, 23)(12, 24)(17, 33)(18, 20)(19, 38)(22, 44)(25, 42)(26, 51)(27, 53)(28, 61)(29, 52)(30, 45)(31, 58)(32, 59)(34, 64)(35, 54)(36, 67)(40, 43)(41, 69)(46, 72)(47, 74)(48, 76)(49, 77)(50, 78)(55, 73)(56, 68)(57, 62)(60, 66)(63, 88)(70, 75)(71, 91)(79, 80)(81, 98)(82, 92)(83, 101)(84, 102)(85, 106)(86, 97)(87, 105)(89, 104)(90, 100)(93, 103)(94, 99)(95, 107)(96, 108)(110, 113)(111, 116)(112, 119)(114, 123)(115, 126)(117, 127)(118, 134)(120, 141)(122, 140)(124, 132)(125, 145)(128, 139)(129, 150)(130, 152)(131, 135)(133, 151)(136, 159)(137, 160)(138, 162)(142, 165)(143, 167)(144, 166)(146, 170)(147, 171)(148, 156)(149, 173)(153, 168)(154, 161)(155, 164)(157, 181)(158, 172)(163, 174)(169, 188)(175, 193)(176, 195)(177, 194)(178, 197)(179, 198)(180, 204)(182, 200)(183, 201)(184, 202)(185, 196)(186, 203)(187, 199)(189, 205)(190, 206)(191, 207)(192, 208)(209, 210)(211, 215)(212, 216)(213, 214)
g: (12, 70)
h: (83, 87)
m: (52, 56)
n1: (101, 107)(105, 108)(198, 203)(201, 206)(209, 211)(213, 216)
a1: (74, 76)
b1: (18, 61)
c1: (64, 67)
d1: (23, 25)
e1: (95, 96)
f1: (49, 89)
g1: (81, 90)(85, 93)(177, 185)(180, 187)(209, 216)(211, 213)
h1: (59, 77)(102, 104)(160, 171)(181, 188)(198, 201)(203, 206)
m1: (34, 36)
n2: (47, 48)
a2: (11, 42)
b2: (20, 28)
c2: (98, 100)(103, 106)(194, 196)(199, 204)(210, 212)(214, 215)
d2: (13, 23)(25, 45)(116, 123)(128, 140)(150, 174)(165, 173)
e2: (15, 24)(54, 75)(119, 126)(134, 145)(152, 159)(167, 170)
f2: (16, 17)
g2: (107, 108)
h2: (8, 16)(17, 66)(119, 134)(120, 127)(126, 145)(132, 135)
m2: (27, 31)
n3: (2, 5)(3, 9)(4, 11)(6, 8)(7, 18)(12, 16)(13, 26)(14, 29)(15, 27)(17, 70)(19, 21)(20, 41)(23, 46)(24, 47)(25, 50)(28, 55)(30, 57)(31, 54)(32, 38)(33, 61)(34, 37)(35, 66)(36, 39)(40, 68)(42, 44)(43, 60)(45, 71)(48, 75)(49, 64)(51, 79)(52, 81)(53, 80)(56, 85)(58, 94)(59, 83)(63, 65)(67, 89)(69, 90)(72, 92)(73, 93)(74, 82)(76, 86)(77, 95)(78, 97)(84, 88)(87, 102)(91, 99)(96, 104)(98, 101)(100, 107)(103, 108)(105, 106)(109, 111)(110, 114)(112, 127)(113, 122)(115, 120)(116, 129)(117, 133)(118, 132)(119, 130)(121, 139)(123, 142)(124, 144)(125, 135)(126, 143)(128, 149)(131, 153)(134, 136)(137, 156)(138, 154)(140, 163)(141, 164)(145, 146)(147, 162)(150, 175)(151, 177)(152, 176)(155, 180)(157, 161)(159, 189)(160, 179)(165, 184)(166, 185)(167, 178)(168, 187)(169, 172)(170, 182)(171, 186)(173, 191)(174, 192)(181, 183)(188, 190)(193, 195)(194, 209)(196, 211)(197, 208)(198, 210)(199, 213)(200, 207)(201, 215)(202, 205)(203, 212)(204, 216)(206, 214)
a3: (32, 49)(84, 89)(137, 147)(157, 169)(179, 183)(186, 190)
b3: (2, 4)(44, 57)(109, 110)(113, 121)(116, 140)(123, 128)
c3: (24, 75)
d3: (14, 20)(28, 40)(117, 124)(131, 141)(151, 155)(166, 168)
e3: (6, 12)(35, 70)(112, 115)(118, 125)(130, 136)(143, 146)
f3: (26, 46)(50, 71)(129, 142)(149, 163)(175, 192)(184, 191)
g3: (7, 33)
h3: (53, 58)
m3: (101, 105)
n4: (100, 103)
a4: (41, 55)
b4: (46, 50)
c4: (38, 64)(67, 88)(156, 162)(160, 181)(161, 172)(171, 188)
d4: (92, 97)
e4: (53, 74)(58, 76)(152, 167)(159, 170)(195, 205)(197, 200)
f4: (21, 37)(39, 65)(138, 158)(148, 154)(156, 161)(162, 172)
g4: (19, 34)(36, 63)(137, 157)(138, 148)(147, 169)(154, 158)
h4: (79, 92)(97, 99)(175, 184)(191, 192)(195, 197)(200, 205)
m4: (3, 7)(33, 60)(112, 118)(115, 125)(117, 141)(124, 131)
n5: (29, 41)(55, 68)(133, 144)(153, 164)(177, 180)(185, 187)
a5: (52, 69)(56, 73)(151, 166)(155, 168)(194, 204)(196, 199)
b5: (90, 93)
c5: (80, 82)(86, 94)(176, 178)(182, 189)(193, 202)(207, 208)
d5: (77, 104)
e5: (82, 86)
f5: (27, 47)(31, 48)(130, 143)(136, 146)(176, 189)(178, 182)
g5: (69, 73)
h5: (83, 95)(87, 96)(179, 186)(183, 190)(210, 215)(212, 214)
m5: (5, 11)(30, 42)(111, 114)(122, 139)(129, 163)(142, 149)
n6: (51, 72)(78, 91)(150, 165)(173, 174)(193, 208)(202, 207)
a6: (72, 78)

(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[ 216, 79 ]
216
-1 110 111 114 109
-2 123 113 116 109
-3 112 124 115 117
-4 110 121 128 140
-5 111 122 129 142
-6 143 112 118 130
-7 125 118 141 131
-8 132 126 127 119
-9 133 144 127 120
-10 121 122 113 139
-11 114 149 139 163
-12 146 125 136 115
-13 165 116 150 140
-14 166 117 151 141
-15 134 167 119 152
-16 134 145 135 120
-17 134 145 135 120
-18 132 135 153 164
-19 154 147 137 148
-20 155 124 168 131
-21 156 148 138 162
-22 121 122 113 139
-23 123 128 173 174
-24 145 126 159 170
-25 123 128 173 174
-26 129 184 163 175
-27 176 178 136 130
-28 155 124 168 131
-29 133 177 185 164
-30 111 122 129 142
-31 176 178 136 130
-32 157 179 137 186
-33 125 118 141 131
-34 157 158 169 138
-35 143 112 118 130
-36 157 158 169 138
-37 154 158 161 172
-38 156 160 171 161
-39 154 158 161 172
-40 166 117 151 141
-41 187 144 180 153
-42 114 149 139 163
-43 133 144 127 120
-44 110 121 128 140
-45 165 116 150 140
-46 191 192 149 142
-47 143 189 146 182
-48 143 189 146 182
-49 190 147 169 183
-50 191 192 149 142
-51 202 193 150 174
-52 155 194 151 196
-53 159 195 152 197
-54 134 167 119 152
-55 187 144 180 153
-56 155 194 151 196
-57 123 113 116 109
-58 159 195 152 197
-59 198 181 203 160
-60 112 124 115 117
-61 132 135 153 164
-62 110 111 114 109
-63 154 147 137 148
-64 188 181 172 162
-65 156 148 138 162
-66 132 126 127 119
-67 188 181 172 162
-68 133 177 185 164
-69 166 199 168 204
-70 146 125 136 115
-71 129 184 163 175
-72 165 173 207 208
-73 166 199 168 204
-74 167 200 170 205
-75 145 126 159 170
-76 167 200 170 205
-77 188 201 171 206
-78 165 173 207 208
-79 192 205 195 175
-80 176 189 193 208
-81 209 177 211 180
-82 178 202 182 207
-83 210 179 212 183
-84 157 179 137 186
-85 209 177 211 180
-86 178 202 182 207
-87 210 179 212 183
-88 156 160 171 161
-89 190 147 169 183
-90 187 213 216 185
-91 202 193 150 174
-92 200 191 184 197
-93 187 213 216 185
-94 176 189 193 208
-95 190 214 215 186
-96 190 214 215 186
-97 200 191 184 197
-98 210 204 215 194
-99 192 205 195 175
-100 199 212 214 196
-101 198 209 201 216
-102 198 181 203 160
-103 199 212 214 196
-104 188 201 171 206
-105 198 209 201 216
-106 210 204 215 194
-107 211 213 203 206
-108 211 213 203 206
-109 1 2 57 62
-110 44 1 4 62
-111 1 5 62 30
-112 35 3 60 6
-113 22 2 57 10
-114 11 1 62 42
-115 12 3 70 60
-116 45 2 13 57
-117 3 14 60 40
-118 33 35 6 7
-119 66 15 8 54
-120 16 17 9 43
-121 22 44 4 10
-122 22 5 30 10
-123 23 2 57 25
-124 3 60 28 20
-125 33 12 70 7
-126 66 24 8 75
-127 66 8 9 43
-128 44 23 25 4
-129 26 5 71 30
-130 35 27 6 31
-131 33 28 7 20
-132 66 61 18 8
-133 68 29 9 43
-134 15 16 17 54
-135 16 17 61 18
-136 12 70 27 31
-137 84 19 63 32
-138 34 36 21 65
-139 11 22 42 10
-140 44 45 13 4
-141 33 14 7 40
-142 46 5 50 30
-143 35 47 48 6
-144 55 41 9 43
-145 24 16 17 75
-146 12 47 48 70
-147 89 49 19 63
-148 19 63 21 65
-149 11 46 50 42
-150 45 13 91 51
-151 56 14 40 52
-152 58 15 53 54
-153 55 61 18 41
-154 37 39 19 63
-155 56 28 52 20
-156 88 38 21 65
-157 34 36 84 32
-158 34 36 37 39
-159 24 58 53 75
-160 88 102 59 38
-161 88 37 38 39
-162 67 64 21 65
-163 11 26 71 42
-164 68 61 18 29
-165 45 78 13 72
-166 14 69 40 73
-167 15 74 54 76
-168 69 28 73 20
-169 34 89 36 49
-170 24 74 75 76
-171 77 88 38 104
-172 67 37 39 64
-173 23 78 25 72
-174 23 25 91 51
-175 99 79 26 71
-176 80 27 94 31
-177 68 81 29 85
-178 27 82 31 86
-179 83 84 32 87
-180 55 81 41 85
-181 67 102 59 64
-182 47 48 82 86
-183 89 49 83 87
-184 26 92 71 97
-185 68 90 93 29
-186 84 95 96 32
-187 55 90 93 41
-188 77 67 104 64
-189 47 80 48 94
-190 89 49 95 96
-191 46 92 50 97
-192 99 46 79 50
-193 80 91 94 51
-194 56 106 52 98
-195 99 79 58 53
-196 56 100 103 52
-197 58 92 53 97
-198 101 102 59 105
-199 100 69 103 73
-200 92 74 97 76
-201 77 101 104 105
-202 91 82 51 86
-203 102 59 107 108
-204 69 73 106 98
-205 99 79 74 76
-206 77 104 107 108
-207 78 82 72 86
-208 78 80 72 94
-209 101 81 105 85
-210 83 106 87 98
-211 81 85 107 108
-212 100 103 83 87
-213 90 93 107 108
-214 100 103 95 96
-215 95 106 96 98
-216 90 101 93 105
0

**************