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On this page are computer-accessible forms for the graph C4[ 168, 22 ] = PL(MSY(4,21,13,0)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {65, 85} under the group generated by the following permutations:

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

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

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