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On this page are computer-accessible forms for the graph C4[ 168, 14 ] = PS(3,56;9).

(I) Following is a form readable by MAGMA:

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

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

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

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