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On this page are computer-accessible forms for the graph C4[ 168, 12 ] = PS(12,28;3).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {56, 57} under the group generated by the following permutations:

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

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

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