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On this page are computer-accessible forms for the graph C4[ 168, 57 ] = XI(Rmap(84,46){3,8|8}_8).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {84, 93} under the group generated by the following permutations:

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

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

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