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On this page are computer-accessible forms for the graph C4[ 168, 21 ] = PX(21,3).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {8, 15} under the group generated by the following permutations:

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

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

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