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On this page are computer-accessible forms for the graph C4[ 164, 4 ] = R_82(43,42).

(I) Following is a form readable by MAGMA:

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

(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: (13, 94)(14, 136)(54, 135)(55, 95)
b: (37, 118)(38, 160)(78, 159)(79, 119)
c: (32, 113)(33, 74)(34, 156)(73, 154)(75, 115)(114, 155)
d: (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)
e: (7, 88)(8, 130)(48, 129)(49, 89)
f: (9, 90)(10, 132)(50, 131)(51, 91)
g: (6, 87)(7, 48)(8, 130)(47, 128)(49, 89)(88, 129)
h: (2, 122, 83, 82)(3, 40, 125, 121)(4, 39)(5, 38)(6, 37)(7, 36)(8, 35)(9, 34)(10, 33)(11, 32)(12, 31)(13, 30)(14, 29)(15, 28)(16, 27)(17, 26)(18, 25)(19, 24)(20, 23)(21, 22)(41, 43, 163, 124)(44, 81, 84, 162)(45, 80)(46, 79)(47, 78)(48, 77)(49, 76)(50, 75)(51, 74)(52, 73)(53, 72)(54, 71)(55, 70)(56, 69)(57, 68)(58, 67)(59, 66)(60, 65)(61, 64)(62, 63)(85, 161)(86, 160)(87, 159)(88, 158)(89, 157)(90, 156)(91, 155)(92, 154)(93, 153)(94, 152)(95, 151)(96, 150)(97, 149)(98, 148)(99, 147)(100, 146)(101, 145)(102, 144)(103, 143)(104, 142)(105, 141)(106, 140)(107, 139)(108, 138)(109, 137)(110, 136)(111, 135)(112, 134)(113, 133)(114, 132)(115, 131)(116, 130)(117, 129)(118, 128)(119, 127)(120, 126)(123, 164)
m: (35, 116)(36, 158)(76, 157)(77, 117)
n1: (39, 120)(40, 162)(80, 161)(81, 121)
a1: (36, 117)(37, 78)(38, 160)(77, 158)(79, 119)(118, 159)
b1: (30, 111)(31, 72)(32, 154)(71, 152)(73, 113)(112, 153)
c1: (4, 85)(5, 46)(6, 128)(45, 126)(47, 87)(86, 127)
d1: (5, 86)(6, 128)(46, 127)(47, 87)
e1: (22, 103)(23, 64)(24, 146)(63, 144)(65, 105)(104, 145)
f1: (19, 100)(20, 142)(60, 141)(61, 101)
g1: (38, 119)(39, 80)(40, 162)(79, 160)(81, 121)(120, 161)
h1: (16, 97)(17, 58)(18, 140)(57, 138)(59, 99)(98, 139)
m1: (10, 91)(11, 52)(12, 134)(51, 132)(53, 93)(92, 133)
n2: (28, 109)(29, 70)(30, 152)(69, 150)(71, 111)(110, 151)
a2: (20, 101)(21, 62)(22, 144)(61, 142)(63, 103)(102, 143)
b2: (15, 96)(16, 138)(56, 137)(57, 97)
c2: (23, 104)(24, 146)(64, 145)(65, 105)
d2: (33, 114)(34, 156)(74, 155)(75, 115)
e2: (25, 106)(26, 148)(66, 147)(67, 107)
f2: (27, 108)(28, 150)(68, 149)(69, 109)
g2: (26, 107)(27, 68)(28, 150)(67, 148)(69, 109)(108, 149)
h2: (34, 115)(35, 76)(36, 158)(75, 156)(77, 117)(116, 157)
m2: (14, 95)(15, 56)(16, 138)(55, 136)(57, 97)(96, 137)
n3: (24, 105)(25, 66)(26, 148)(65, 146)(67, 107)(106, 147)
a3: (21, 102)(22, 144)(62, 143)(63, 103)
b3: (11, 92)(12, 134)(52, 133)(53, 93)
c3: (17, 98)(18, 140)(58, 139)(59, 99)
d3: (31, 112)(32, 154)(72, 153)(73, 113)
e3: (18, 99)(19, 60)(20, 142)(59, 140)(61, 101)(100, 141)
f3: (12, 93)(13, 54)(14, 136)(53, 134)(55, 95)(94, 135)
g3: (29, 110)(30, 152)(70, 151)(71, 111)
h3: (40, 121)(41, 163)(81, 162)(82, 122)
m3: (8, 89)(9, 50)(10, 132)(49, 130)(51, 91)(90, 131)

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

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