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On this page are computer-accessible forms for the graph C4[ 216, 75 ] = SDD(AMC(6,3,[0.1:2.2])).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {104, 121} under the group generated by the following permutations:

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

(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.

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&Graph
C4[ 216, 75 ]
216
-1 110 111 113 109
-2 112 114 117 109
-3 110 123 115 118
-4 111 124 116 119
-5 133 112 125 120
-6 121 134 113 126
-7 122 135 114 127
-8 136 147 115 128
-9 137 148 116 129
-10 138 149 117 130
-11 139 150 118 131
-12 132 140 151 119
-13 166 128 152 120
-14 121 167 141 153
-15 122 137 142 164
-16 143 154 123 168
-17 144 155 124 169
-18 132 145 125 159
-19 156 146 126 170
-20 156 127 139 140
-21 188 171 129 141
-22 189 157 172 130
-23 158 185 131 153
-24 133 190 160 173
-25 134 191 161 174
-26 187 155 135 162
-27 178 146 136 163
-28 165 138 183 151
-29 156 127 139 140
-30 157 192 206 142
-31 143 193 207 175
-32 176 144 194 208
-33 177 145 172 185
-34 209 179 147 195
-35 180 148 184 196
-36 191 181 149 197
-37 182 150 205 174
-38 165 138 183 151
-39 165 200 184 152
-40 154 170 204 186
-41 187 155 135 162
-42 132 140 151 119
-43 211 158 181 175
-44 176 159 214 197
-45 198 180 160 207
-46 198 177 199 161
-47 210 182 162 196
-48 193 194 163 164
-49 166 201 212 186
-50 210 167 201 202
-51 168 169 192 203
-52 168 169 192 203
-53 154 170 204 186
-54 156 146 126 170
-55 187 190 213 171
-56 204 183 173 195
-57 182 150 205 174
-58 144 155 124 169
-59 122 135 114 127
-60 199 178 203 215
-61 189 179 202 208
-62 209 188 205 216
-63 191 181 149 197
-64 187 190 213 171
-65 204 183 173 195
-66 139 150 118 131
-67 176 159 214 197
-68 134 191 161 174
-69 138 149 117 130
-70 111 124 116 119
-71 200 211 213 215
-72 212 214 216 206
-73 209 188 205 216
-74 165 200 184 152
-75 210 182 162 196
-76 132 145 125 159
-77 199 178 203 215
-78 157 192 206 142
-79 143 154 123 168
-80 121 134 113 126
-81 112 114 117 109
-82 200 211 213 215
-83 212 214 216 206
-84 166 201 212 186
-85 178 146 136 163
-86 176 144 194 208
-87 122 137 142 164
-88 211 158 181 175
-89 188 171 129 141
-90 133 190 160 173
-91 110 123 115 118
-92 110 111 113 109
-93 209 179 147 195
-94 158 185 131 153
-95 198 177 199 161
-96 189 157 172 130
-97 137 148 116 129
-98 166 128 152 120
-99 180 148 184 196
-100 133 112 125 120
-101 210 167 201 202
-102 177 145 172 185
-103 143 193 207 175
-104 121 167 141 153
-105 136 147 115 128
-106 193 194 163 164
-107 189 179 202 208
-108 198 180 160 207
-109 1 2 81 92
-110 1 3 91 92
-111 1 4 70 92
-112 100 2 81 5
-113 1 80 92 6
-114 2 59 81 7
-115 3 91 105 8
-116 4 70 9 97
-117 2 69 81 10
-118 11 66 3 91
-119 12 4 70 42
-120 100 13 5 98
-121 14 80 104 6
-122 15 59 7 87
-123 79 3 91 16
-124 58 4 70 17
-125 100 5 18 76
-126 80 6 19 54
-127 59 7 29 20
-128 13 105 8 98
-129 89 9 97 21
-130 22 69 96 10
-131 11 66 23 94
-132 12 18 42 76
-133 100 24 90 5
-134 68 25 80 6
-135 26 59 7 41
-136 27 105 8 85
-137 15 9 97 87
-138 69 38 28 10
-139 11 66 29 20
-140 12 29 20 42
-141 89 14 104 21
-142 78 15 30 87
-143 79 103 16 31
-144 58 17 86 32
-145 33 102 18 76
-146 27 19 85 54
-147 34 93 105 8
-148 99 35 9 97
-149 36 69 63 10
-150 11 66 57 37
-151 12 38 28 42
-152 13 39 74 98
-153 23 14 104 94
-154 79 16 40 53
-155 58 26 17 41
-156 29 19 20 54
-157 22 78 30 96
-158 88 23 94 43
-159 44 67 18 76
-160 45 24 90 108
-161 46 68 25 95
-162 47 26 41 75
-163 48 27 106 85
-164 15 48 106 87
-165 38 28 39 74
-166 13 49 84 98
-167 101 14 104 50
-168 79 16 51 52
-169 58 17 51 52
-170 40 19 53 54
-171 55 89 64 21
-172 22 33 102 96
-173 56 24 90 65
-174 57 68 25 37
-175 88 103 31 43
-176 44 67 86 32
-177 33 46 102 95
-178 77 27 60 85
-179 34 93 61 107
-180 99 45 35 108
-181 88 36 63 43
-182 57 47 37 75
-183 56 38 28 65
-184 99 35 39 74
-185 33 23 102 94
-186 49 40 84 53
-187 55 26 41 64
-188 89 62 73 21
-189 22 61 96 107
-190 55 24 90 64
-191 68 25 36 63
-192 78 51 30 52
-193 48 103 106 31
-194 48 106 86 32
-195 34 56 93 65
-196 99 35 47 75
-197 44 67 36 63
-198 45 46 95 108
-199 77 46 60 95
-200 71 82 39 74
-201 101 49 50 84
-202 101 50 61 107
-203 77 60 51 52
-204 56 40 53 65
-205 57 37 62 73
-206 78 72 83 30
-207 45 103 31 108
-208 61 107 86 32
-209 34 93 62 73
-210 101 47 50 75
-211 88 71 82 43
-212 49 72 83 84
-213 55 71 82 64
-214 44 67 72 83
-215 77 60 71 82
-216 72 83 62 73
0

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