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On this page are computer-accessible forms for the graph C4[ 168, 20 ] = R_84(23,64).

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

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

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

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