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On this page are computer-accessible forms for the graph C4[ 168, 19 ] = R_84(65,22).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {2, 3} under the group generated by the following permutations:

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

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

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