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On this page are computer-accessible forms for the graph C4[ 168, 58 ] = SDD(W(21,2)).

(I) Following is a form readable by MAGMA:

g:=Graph<168|{ {79, 101}, {83, 121}, {70, 109}, {65, 114}, {71, 116}, {75, 114}, {80, 105}, {65, 123}, {64, 123}, {71, 124}, {79, 115}, {65, 124}, {41, 105}, {55, 119}, {56, 120}, {58, 122}, {59, 123}, {42, 107}, {62, 127}, {60, 125}, {36, 102}, {61, 127}, {56, 122}, {58, 120}, {36, 103}, {54, 117}, {26, 94}, {28, 88}, {58, 126}, {35, 102}, {19, 85}, {56, 126}, {36, 108}, {54, 126}, {52, 125}, {57, 112}, {19, 89}, {32, 106}, {51, 121}, {55, 125}, {16, 91}, {60, 119}, {41, 98}, {35, 111}, {33, 108}, {16, 94}, {17, 95}, {19, 92}, {37, 106}, {34, 109}, {25, 86}, {53, 101}, {32, 113}, {4, 86}, {15, 93}, {14, 92}, {11, 89}, {5, 87}, {10, 89}, {39, 116}, {13, 94}, {51, 96}, {1, 85}, {38, 114}, {37, 113}, {51, 103}, {42, 127}, {1, 87}, {13, 91}, {12, 90}, {47, 121}, {1, 86}, {33, 118}, {8, 95}, {2, 85}, {3, 91}, {44, 116}, {7, 94}, {52, 110}, {1, 90}, {3, 88}, {2, 89}, {2, 92}, {6, 88}, {3, 93}, {41, 119}, {51, 109}, {16, 113}, {17, 112}, {12, 110}, {20, 118}, {18, 112}, {21, 118}, {7, 99}, {28, 120}, {24, 124}, {23, 115}, {22, 114}, {18, 118}, {15, 107}, {10, 110}, {9, 109}, {8, 108}, {4, 97}, {21, 112}, {11, 110}, {6, 99}, {2, 100}, {3, 101}, {57, 95}, {5, 98}, {10, 98}, {53, 93}, {9, 96}, {26, 115}, {11, 98}, {11, 97}, {22, 124}, {16, 122}, {54, 92}, {10, 97}, {4, 104}, {25, 117}, {24, 116}, {7, 107}, {6, 106}, {5, 105}, {22, 123}, {53, 88}, {8, 102}, {9, 103}, {52, 90}, {53, 91}, {8, 103}, {9, 121}, {15, 127}, {14, 126}, {4, 117}, {26, 107}, {25, 104}, {12, 125}, {5, 119}, {29, 111}, {23, 101}, {18, 96}, {40, 90}, {27, 104}, {7, 115}, {21, 96}, {28, 106}, {31, 105}, {30, 104}, {13, 122}, {19, 100}, {42, 93}, {20, 108}, {25, 97}, {26, 99}, {21, 111}, {30, 100}, {14, 117}, {36, 95}, {29, 102}, {13, 113}, {18, 111}, {40, 85}, {6, 120}, {40, 86}, {41, 87}, {27, 100}, {28, 99}, {40, 87}, {17, 145}, {14, 143}, {12, 142}, {38, 164}, {27, 152}, {23, 146}, {34, 167}, {30, 152}, {29, 148}, {30, 151}, {47, 166}, {24, 147}, {31, 148}, {27, 151}, {31, 145}, {17, 128}, {31, 142}, {59, 168}, {22, 130}, {23, 131}, {20, 129}, {61, 168}, {62, 168}, {59, 163}, {61, 164}, {29, 135}, {62, 164}, {24, 132}, {20, 138}, {15, 144}, {33, 129}, {38, 134}, {43, 139}, {56, 152}, {39, 134}, {39, 133}, {46, 140}, {58, 152}, {34, 129}, {35, 135}, {63, 155}, {45, 137}, {50, 150}, {45, 136}, {47, 138}, {44, 139}, {46, 137}, {49, 150}, {57, 145}, {43, 130}, {63, 150}, {44, 133}, {50, 155}, {37, 143}, {44, 134}, {33, 138}, {48, 155}, {39, 139}, {49, 157}, {32, 143}, {48, 159}, {43, 155}, {55, 135}, {45, 156}, {47, 158}, {37, 151}, {63, 141}, {48, 130}, {46, 157}, {43, 159}, {50, 132}, {32, 151}, {35, 148}, {55, 128}, {45, 149}, {46, 150}, {49, 137}, {54, 143}, {57, 128}, {42, 144}, {52, 142}, {34, 153}, {63, 132}, {60, 135}, {48, 139}, {38, 154}, {60, 128}, {49, 140}, {62, 131}, {59, 133}, {61, 131}, {50, 141}, {80, 145}, {84, 149}, {81, 144}, {65, 130}, {81, 146}, {71, 132}, {76, 136}, {80, 148}, {64, 133}, {72, 141}, {74, 140}, {70, 129}, {82, 149}, {68, 140}, {69, 141}, {66, 136}, {67, 137}, {67, 136}, {81, 154}, {79, 131}, {75, 134}, {83, 158}, {75, 154}, {78, 159}, {76, 158}, {78, 157}, {71, 147}, {73, 157}, {72, 156}, {76, 153}, {67, 149}, {73, 159}, {77, 154}, {69, 156}, {83, 138}, {73, 147}, {66, 153}, {66, 158}, {77, 144}, {79, 146}, {78, 147}, {80, 142}, {67, 156}, {77, 146}, {70, 153}, {66, 162}, {69, 165}, {70, 167}, {64, 163}, {68, 160}, {69, 161}, {68, 161}, {68, 162}, {64, 168}, {74, 162}, {72, 161}, {74, 160}, {74, 161}, {78, 165}, {73, 165}, {72, 165}, {76, 162}, {77, 163}, {75, 164}, {81, 163}, {84, 166}, {82, 160}, {84, 167}, {82, 166}, {84, 160}, {82, 167}, {83, 166} }>;

(II) A more general form is to represent the graph as the orbit of {79, 101} under the group generated by the following permutations:

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

(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[ 168, 58 ]
168
-1 90 85 86 87
-2 89 100 92 85
-3 88 101 91 93
-4 104 117 86 97
-5 105 119 87 98
-6 88 99 106 120
-7 99 115 94 107
-8 102 103 95 108
-9 121 103 96 109
-10 110 89 97 98
-11 110 89 97 98
-12 110 90 125 142
-13 122 91 113 94
-14 143 92 126 117
-15 144 93 127 107
-16 122 91 113 94
-17 112 145 95 128
-18 111 112 96 118
-19 89 100 92 85
-20 138 118 129 108
-21 111 112 96 118
-22 123 124 114 130
-23 101 146 115 131
-24 132 124 147 116
-25 104 117 86 97
-26 99 115 94 107
-27 100 104 151 152
-28 88 99 106 120
-29 111 102 135 148
-30 100 104 151 152
-31 145 148 105 142
-32 143 113 106 151
-33 138 118 129 108
-34 167 129 109 153
-35 111 102 135 148
-36 102 103 95 108
-37 143 113 106 151
-38 154 134 114 164
-39 133 134 116 139
-40 90 85 86 87
-41 105 119 87 98
-42 144 93 127 107
-43 155 159 139 130
-44 133 134 116 139
-45 156 136 137 149
-46 157 137 150 140
-47 121 166 158 138
-48 155 159 139 130
-49 157 137 150 140
-50 132 155 150 141
-51 121 103 96 109
-52 110 90 125 142
-53 88 101 91 93
-54 143 92 126 117
-55 135 125 128 119
-56 122 126 152 120
-57 112 145 95 128
-58 122 126 152 120
-59 133 123 168 163
-60 135 125 128 119
-61 168 127 131 164
-62 168 127 131 164
-63 132 155 150 141
-64 133 123 168 163
-65 123 124 114 130
-66 136 158 162 153
-67 156 136 137 149
-68 160 161 140 162
-69 165 156 161 141
-70 167 129 109 153
-71 132 124 147 116
-72 165 156 161 141
-73 165 157 147 159
-74 160 161 140 162
-75 154 134 114 164
-76 136 158 162 153
-77 154 144 146 163
-78 165 157 147 159
-79 101 146 115 131
-80 145 148 105 142
-81 154 144 146 163
-82 166 167 149 160
-83 121 166 158 138
-84 166 167 149 160
-85 1 2 40 19
-86 1 25 4 40
-87 1 5 40 41
-88 3 6 28 53
-89 11 2 19 10
-90 1 12 40 52
-91 13 3 16 53
-92 2 14 19 54
-93 3 15 42 53
-94 13 26 16 7
-95 57 36 17 8
-96 18 51 9 21
-97 11 25 4 10
-98 11 5 41 10
-99 26 6 28 7
-100 2 27 19 30
-101 23 79 3 53
-102 35 36 29 8
-103 36 51 8 9
-104 25 4 27 30
-105 80 5 41 31
-106 37 6 28 32
-107 15 26 7 42
-108 33 36 8 20
-109 34 70 51 9
-110 11 12 52 10
-111 35 18 29 21
-112 57 17 18 21
-113 13 37 16 32
-114 22 38 75 65
-115 23 79 26 7
-116 44 24 71 39
-117 14 25 4 54
-118 33 18 20 21
-119 55 5 60 41
-120 56 58 6 28
-121 47 83 51 9
-122 56 13 58 16
-123 22 59 64 65
-124 22 24 71 65
-125 55 12 60 52
-126 56 14 58 54
-127 15 61 62 42
-128 55 57 60 17
-129 33 34 70 20
-130 22 48 43 65
-131 23 79 61 62
-132 24 71 50 63
-133 44 59 39 64
-134 44 38 39 75
-135 55 35 60 29
-136 66 45 67 76
-137 45 67 46 49
-138 33 47 83 20
-139 44 48 39 43
-140 46 68 49 74
-141 69 50 72 63
-142 12 80 52 31
-143 14 37 32 54
-144 77 15 81 42
-145 57 80 17 31
-146 77 23 79 81
-147 78 24 71 73
-148 35 80 29 31
-149 45 67 82 84
-150 46 49 50 63
-151 37 27 30 32
-152 56 58 27 30
-153 66 34 70 76
-154 77 81 38 75
-155 48 50 63 43
-156 45 67 69 72
-157 78 46 49 73
-158 66 47 83 76
-159 78 48 73 43
-160 68 82 84 74
-161 68 69 72 74
-162 66 68 74 76
-163 77 59 81 64
-164 38 61 62 75
-165 78 69 72 73
-166 47 82 83 84
-167 34 70 82 84
-168 59 61 62 64
0

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