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On this page are computer-accessible forms for the graph C4[ 172, 2 ] = R_86(45,44).

(I) Following is a form readable by MAGMA:

g:=Graph<172|{ {2, 3}, {54, 55}, {52, 53}, {50, 51}, {48, 49}, {46, 47}, {44, 45}, {42, 43}, {40, 41}, {38, 39}, {36, 37}, {34, 35}, {32, 33}, {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}, {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}, {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}, {85, 86}, {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}, {15, 16}, {47, 48}, {79, 80}, {64, 105}, {66, 107}, {68, 109}, {70, 111}, {80, 121}, {82, 123}, {84, 125}, {86, 127}, {128, 170}, {129, 171}, {65, 106}, {69, 110}, {81, 122}, {85, 126}, {128, 172}, {130, 172}, {67, 108}, {83, 124}, {71, 112}, {79, 120}, {72, 113}, {74, 115}, {76, 117}, {78, 119}, {73, 114}, {77, 118}, {31, 32}, {75, 116}, {1, 87}, {41, 127}, {40, 126}, {33, 119}, {32, 118}, {8, 94}, {9, 95}, {1, 86}, {55, 96}, {63, 104}, {56, 97}, {58, 99}, {60, 101}, {62, 103}, {2, 88}, {39, 125}, {38, 124}, {35, 121}, {34, 120}, {3, 89}, {6, 92}, {7, 93}, {57, 98}, {61, 102}, {4, 90}, {37, 123}, {36, 122}, {5, 91}, {59, 100}, {48, 89}, {52, 93}, {50, 91}, {54, 95}, {10, 96}, {11, 97}, {14, 100}, {15, 101}, {26, 112}, {27, 113}, {30, 116}, {31, 117}, {49, 90}, {53, 94}, {12, 98}, {13, 99}, {28, 114}, {29, 115}, {51, 92}, {16, 102}, {17, 103}, {24, 110}, {25, 111}, {47, 88}, {46, 87}, {18, 104}, {19, 105}, {22, 108}, {23, 109}, {20, 106}, {21, 107}, {63, 64}, {1, 128}, {45, 172}, {43, 170}, {41, 168}, {39, 166}, {37, 164}, {35, 162}, {33, 160}, {3, 130}, {5, 132}, {7, 134}, {9, 136}, {11, 138}, {13, 140}, {15, 142}, {17, 144}, {19, 146}, {21, 148}, {23, 150}, {25, 152}, {27, 154}, {29, 156}, {31, 158}, {2, 129}, {42, 169}, {38, 165}, {34, 161}, {6, 133}, {10, 137}, {14, 141}, {18, 145}, {22, 149}, {26, 153}, {30, 157}, {4, 131}, {44, 171}, {36, 163}, {12, 139}, {20, 147}, {28, 155}, {8, 135}, {40, 167}, {24, 151}, {16, 143}, {42, 128}, {47, 133}, {46, 132}, {43, 129}, {58, 144}, {59, 145}, {62, 148}, {63, 149}, {44, 130}, {45, 131}, {60, 146}, {61, 147}, {48, 134}, {49, 135}, {56, 142}, {57, 143}, {50, 136}, {51, 137}, {54, 140}, {55, 141}, {52, 138}, {53, 139}, {32, 159}, {87, 131}, {127, 171}, {126, 170}, {125, 169}, {124, 168}, {119, 163}, {118, 162}, {117, 161}, {116, 160}, {92, 136}, {93, 137}, {94, 138}, {95, 139}, {64, 150}, {127, 169}, {126, 168}, {119, 161}, {118, 160}, {65, 151}, {72, 158}, {73, 159}, {87, 129}, {94, 136}, {95, 137}, {66, 152}, {125, 167}, {124, 166}, {121, 163}, {120, 162}, {67, 153}, {70, 156}, {71, 157}, {88, 130}, {89, 131}, {92, 134}, {93, 135}, {88, 132}, {123, 167}, {122, 166}, {121, 165}, {120, 164}, {89, 133}, {90, 134}, {91, 135}, {68, 154}, {123, 165}, {122, 164}, {69, 155}, {90, 132}, {91, 133}, {74, 160}, {117, 159}, {116, 158}, {113, 155}, {112, 154}, {101, 143}, {100, 142}, {75, 161}, {78, 164}, {79, 165}, {96, 138}, {97, 139}, {96, 140}, {115, 159}, {114, 158}, {113, 157}, {112, 156}, {99, 143}, {97, 141}, {98, 142}, {76, 162}, {115, 157}, {114, 156}, {99, 141}, {77, 163}, {98, 140}, {100, 144}, {111, 155}, {110, 154}, {109, 153}, {108, 152}, {103, 147}, {102, 146}, {101, 145}, {80, 166}, {111, 153}, {110, 152}, {103, 145}, {102, 144}, {81, 167}, {82, 168}, {109, 151}, {108, 150}, {105, 147}, {104, 146}, {83, 169}, {86, 172}, {104, 148}, {107, 151}, {106, 150}, {105, 149}, {84, 170}, {107, 149}, {106, 148}, {85, 171} }>;

(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: (41, 126)(42, 170)(84, 169)(85, 127)
b: (31, 116)(32, 160)(74, 159)(75, 117)
c: (36, 121)(37, 80)(38, 166)(79, 164)(81, 123)(122, 165)
d: (6, 91)(7, 50)(8, 136)(49, 134)(51, 93)(92, 135)
e: (24, 109)(25, 68)(26, 154)(67, 152)(69, 111)(110, 153)
f: (32, 117)(33, 76)(34, 162)(75, 160)(77, 119)(118, 161)
g: (26, 111)(27, 70)(28, 156)(69, 154)(71, 113)(112, 155)
h: (2, 128, 87, 86)(3, 42, 131, 127)(4, 41)(5, 40)(6, 39)(7, 38)(8, 37)(9, 36)(10, 35)(11, 34)(12, 33)(13, 32)(14, 31)(15, 30)(16, 29)(17, 28)(18, 27)(19, 26)(20, 25)(21, 24)(22, 23)(43, 45, 171, 130)(46, 85, 88, 170)(47, 84)(48, 83)(49, 82)(50, 81)(51, 80)(52, 79)(53, 78)(54, 77)(55, 76)(56, 75)(57, 74)(58, 73)(59, 72)(60, 71)(61, 70)(62, 69)(63, 68)(64, 67)(65, 66)(89, 169)(90, 168)(91, 167)(92, 166)(93, 165)(94, 164)(95, 163)(96, 162)(97, 161)(98, 160)(99, 159)(100, 158)(101, 157)(102, 156)(103, 155)(104, 154)(105, 153)(106, 152)(107, 151)(108, 150)(109, 149)(110, 148)(111, 147)(112, 146)(113, 145)(114, 144)(115, 143)(116, 142)(117, 141)(118, 140)(119, 139)(120, 138)(121, 137)(122, 136)(123, 135)(124, 134)(125, 133)(126, 132)(129, 172)
m: (27, 112)(28, 156)(70, 155)(71, 113)
n1: (29, 114)(30, 158)(72, 157)(73, 115)
a1: (33, 118)(34, 162)(76, 161)(77, 119)
b1: (14, 99)(15, 58)(16, 144)(57, 142)(59, 101)(100, 143)
c1: (34, 119)(35, 78)(36, 164)(77, 162)(79, 121)(120, 163)
d1: (15, 100)(16, 144)(58, 143)(59, 101)
e1: (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, 169, 170, 171, 172)
f1: (37, 122)(38, 166)(80, 165)(81, 123)
g1: (11, 96)(12, 140)(54, 139)(55, 97)
h1: (28, 113)(29, 72)(30, 158)(71, 156)(73, 115)(114, 157)
m1: (7, 92)(8, 136)(50, 135)(51, 93)
n2: (40, 125)(41, 84)(42, 170)(83, 168)(85, 127)(126, 169)
a2: (30, 115)(31, 74)(32, 160)(73, 158)(75, 117)(116, 159)
b2: (9, 94)(10, 138)(52, 137)(53, 95)
c2: (19, 104)(20, 148)(62, 147)(63, 105)
d2: (17, 102)(18, 146)(60, 145)(61, 103)
e2: (16, 101)(17, 60)(18, 146)(59, 144)(61, 103)(102, 145)
f2: (38, 123)(39, 82)(40, 168)(81, 166)(83, 125)(124, 167)
g2: (10, 95)(11, 54)(12, 140)(53, 138)(55, 97)(96, 139)
h2: (35, 120)(36, 164)(78, 163)(79, 121)
m2: (20, 105)(21, 64)(22, 150)(63, 148)(65, 107)(106, 149)
n3: (4, 89)(5, 48)(6, 134)(47, 132)(49, 91)(90, 133)
a3: (39, 124)(40, 168)(82, 167)(83, 125)
b3: (21, 106)(22, 150)(64, 149)(65, 107)
c3: (12, 97)(13, 56)(14, 142)(55, 140)(57, 99)(98, 141)
d3: (13, 98)(14, 142)(56, 141)(57, 99)
e3: (8, 93)(9, 52)(10, 138)(51, 136)(53, 95)(94, 137)
f3: (22, 107)(23, 66)(24, 152)(65, 150)(67, 109)(108, 151)
g3: (23, 108)(24, 152)(66, 151)(67, 109)
h3: (5, 90)(6, 134)(48, 133)(49, 91)
m3: (25, 110)(26, 154)(68, 153)(69, 111)
n4: (42, 127)(43, 171)(85, 170)(86, 128)
a4: (18, 103)(19, 62)(20, 148)(61, 146)(63, 105)(104, 147)

(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[ 172, 2 ]
172
-1 2 128 86 87
-2 88 1 3 129
-3 89 2 4 130
-4 90 3 5 131
-5 132 91 4 6
-6 133 92 5 7
-7 134 93 6 8
-8 135 94 7 9
-9 136 95 8 10
-10 11 137 96 9
-11 12 138 97 10
-12 11 13 139 98
-13 99 12 14 140
-14 100 13 15 141
-15 101 14 16 142
-16 143 102 15 17
-17 144 103 16 18
-18 145 104 17 19
-19 146 105 18 20
-20 147 106 19 21
-21 22 148 107 20
-22 23 149 108 21
-23 22 24 150 109
-24 110 23 25 151
-25 111 24 26 152
-26 112 25 27 153
-27 154 113 26 28
-28 155 114 27 29
-29 156 115 28 30
-30 157 116 29 31
-31 158 117 30 32
-32 33 159 118 31
-33 34 160 119 32
-34 33 35 161 120
-35 121 34 36 162
-36 122 35 37 163
-37 123 36 38 164
-38 165 124 37 39
-39 166 125 38 40
-40 167 126 39 41
-41 168 127 40 42
-42 169 128 41 43
-43 44 170 129 42
-44 45 171 130 43
-45 44 46 172 131
-46 132 45 47 87
-47 88 133 46 48
-48 89 134 47 49
-49 90 135 48 50
-50 91 136 49 51
-51 92 137 50 52
-52 93 138 51 53
-53 94 139 52 54
-54 55 95 140 53
-55 56 96 141 54
-56 55 57 97 142
-57 143 56 58 98
-58 99 144 57 59
-59 100 145 58 60
-60 101 146 59 61
-61 102 147 60 62
-62 103 148 61 63
-63 104 149 62 64
-64 105 150 63 65
-65 66 106 151 64
-66 67 107 152 65
-67 66 68 108 153
-68 154 67 69 109
-69 110 155 68 70
-70 111 156 69 71
-71 112 157 70 72
-72 113 158 71 73
-73 114 159 72 74
-74 115 160 73 75
-75 116 161 74 76
-76 77 117 162 75
-77 78 118 163 76
-78 77 79 119 164
-79 165 78 80 120
-80 121 166 79 81
-81 122 167 80 82
-82 123 168 81 83
-83 124 169 82 84
-84 125 170 83 85
-85 126 171 84 86
-86 1 127 172 85
-87 1 46 129 131
-88 132 2 47 130
-89 133 3 48 131
-90 132 134 4 49
-91 133 135 5 50
-92 134 136 6 51
-93 135 137 7 52
-94 136 138 8 53
-95 137 139 9 54
-96 55 138 140 10
-97 11 56 139 141
-98 12 57 140 142
-99 143 13 58 141
-100 144 14 59 142
-101 143 145 15 60
-102 144 146 16 61
-103 145 147 17 62
-104 146 148 18 63
-105 147 149 19 64
-106 148 150 20 65
-107 66 149 151 21
-108 22 67 150 152
-109 23 68 151 153
-110 154 24 69 152
-111 155 25 70 153
-112 154 156 26 71
-113 155 157 27 72
-114 156 158 28 73
-115 157 159 29 74
-116 158 160 30 75
-117 159 161 31 76
-118 77 160 162 32
-119 33 78 161 163
-120 34 79 162 164
-121 165 35 80 163
-122 166 36 81 164
-123 165 167 37 82
-124 166 168 38 83
-125 167 169 39 84
-126 168 170 40 85
-127 169 171 41 86
-128 1 170 172 42
-129 2 171 43 87
-130 44 88 3 172
-131 45 89 4 87
-132 88 46 90 5
-133 89 47 91 6
-134 90 48 92 7
-135 91 49 93 8
-136 92 50 94 9
-137 93 51 95 10
-138 11 94 52 96
-139 12 95 53 97
-140 13 96 54 98
-141 55 99 14 97
-142 56 100 15 98
-143 99 57 101 16
-144 100 58 102 17
-145 101 59 103 18
-146 102 60 104 19
-147 103 61 105 20
-148 104 62 106 21
-149 22 105 63 107
-150 23 106 64 108
-151 24 107 65 109
-152 66 110 25 108
-153 67 111 26 109
-154 110 68 112 27
-155 111 69 113 28
-156 112 70 114 29
-157 113 71 115 30
-158 114 72 116 31
-159 115 73 117 32
-160 33 116 74 118
-161 34 117 75 119
-162 35 118 76 120
-163 77 121 36 119
-164 78 122 37 120
-165 121 79 123 38
-166 122 80 124 39
-167 123 81 125 40
-168 124 82 126 41
-169 125 83 127 42
-170 126 84 128 43
-171 44 127 85 129
-172 45 128 86 130
0

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