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On this page are computer-accessible forms for the graph C4[ 216, 76 ] = SDD(MC3(6,9,1,6,2,0,1)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {96, 109} under the group generated by the following permutations:

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

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

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