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On this page are computer-accessible forms for the graph C4[ 216, 77 ] = SDD(DW(18,3)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {100, 117} under the group generated by the following permutations:

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

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

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