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On this page are computer-accessible forms for the graph C4[ 168, 18 ] = R_84(44,43).

(I) Following is a form readable by MAGMA:

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

(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: (31, 114)(32, 157)(73, 156)(74, 115)
b: (14, 97)(15, 57)(16, 141)(56, 139)(58, 99)(98, 140)
c: (17, 100)(18, 143)(59, 142)(60, 101)
d: (9, 92)(10, 135)(51, 134)(52, 93)
e: (29, 112)(30, 155)(71, 154)(72, 113)
f: (8, 91)(9, 51)(10, 135)(50, 133)(52, 93)(92, 134)
g: (19, 102)(20, 145)(61, 144)(62, 103)
h: (40, 123)(41, 83)(42, 167)(82, 165)(84, 125)(124, 166)
m: (5, 88)(6, 131)(47, 130)(48, 89)
n1: (35, 118)(36, 161)(77, 160)(78, 119)
a1: (34, 117)(35, 77)(36, 161)(76, 159)(78, 119)(118, 160)
b1: (21, 104)(22, 147)(63, 146)(64, 105)
c1: (13, 96)(14, 139)(55, 138)(56, 97)
d1: (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)
e1: (30, 113)(31, 73)(32, 157)(72, 155)(74, 115)(114, 156)
f1: (32, 115)(33, 75)(34, 159)(74, 157)(76, 117)(116, 158)
g1: (6, 89)(7, 49)(8, 133)(48, 131)(50, 91)(90, 132)
h1: (23, 106)(24, 149)(65, 148)(66, 107)
m1: (11, 94)(12, 137)(53, 136)(54, 95)
n2: (41, 124)(42, 167)(83, 166)(84, 125)
a2: (10, 93)(11, 53)(12, 137)(52, 135)(54, 95)(94, 136)
b2: (22, 105)(23, 65)(24, 149)(64, 147)(66, 107)(106, 148)
c2: (18, 101)(19, 61)(20, 145)(60, 143)(62, 103)(102, 144)
d2: (37, 120)(38, 163)(79, 162)(80, 121)
e2: (7, 90)(8, 133)(49, 132)(50, 91)
f2: (20, 103)(21, 63)(22, 147)(62, 145)(64, 105)(104, 146)
g2: (33, 116)(34, 159)(75, 158)(76, 117)
h2: (25, 108)(26, 151)(67, 150)(68, 109)
m2: (15, 98)(16, 141)(57, 140)(58, 99)
n3: (26, 109)(27, 69)(28, 153)(68, 151)(70, 111)(110, 152)
a3: (4, 87)(5, 47)(6, 131)(46, 129)(48, 89)(88, 130)
b3: (38, 121)(39, 81)(40, 165)(80, 163)(82, 123)(122, 164)
c3: (39, 122)(40, 165)(81, 164)(82, 123)
d3: (12, 95)(13, 55)(14, 139)(54, 137)(56, 97)(96, 138)
e3: (36, 119)(37, 79)(38, 163)(78, 161)(80, 121)(120, 162)
f3: (16, 99)(17, 59)(18, 143)(58, 141)(60, 101)(100, 142)
g3: (27, 110)(28, 153)(69, 152)(70, 111)
h3: (24, 107)(25, 67)(26, 151)(66, 149)(68, 109)(108, 150)
m3: (2, 125)(3, 41)(4, 40)(5, 39)(6, 38)(7, 37)(8, 36)(9, 35)(10, 34)(11, 33)(12, 32)(13, 31)(14, 30)(15, 29)(16, 28)(17, 27)(18, 26)(19, 25)(20, 24)(21, 23)(42, 127)(44, 167)(45, 83)(46, 82)(47, 81)(48, 80)(49, 79)(50, 78)(51, 77)(52, 76)(53, 75)(54, 74)(55, 73)(56, 72)(57, 71)(58, 70)(59, 69)(60, 68)(61, 67)(62, 66)(63, 65)(84, 85)(86, 166)(87, 165)(88, 164)(89, 163)(90, 162)(91, 161)(92, 160)(93, 159)(94, 158)(95, 157)(96, 156)(97, 155)(98, 154)(99, 153)(100, 152)(101, 151)(102, 150)(103, 149)(104, 148)(105, 147)(106, 146)(107, 145)(108, 144)(109, 143)(110, 142)(111, 141)(112, 140)(113, 139)(114, 138)(115, 137)(116, 136)(117, 135)(118, 134)(119, 133)(120, 132)(121, 131)(122, 130)(123, 129)(124, 128)(126, 168)
n4: (28, 111)(29, 71)(30, 155)(70, 153)(72, 113)(112, 154)

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

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