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On this page are computer-accessible forms for the graph C4[ 168, 25 ] = PL(MC3(6,14,1,8,3,7,2),[4^21,6^14]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {83, 86} under the group generated by the following permutations:

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

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

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