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On this page are computer-accessible forms for the graph C4[ 162, 1 ] = W(81,2).

(I) Following is a form readable by MAGMA:

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

(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: (22, 103)
b: (69, 150)
c: (15, 96)
d: (78, 159)
e: (26, 107)
f: (32, 113)
g: (79, 160)
h: (30, 111)
m: (29, 110)
n1: (73, 154)
a1: (39, 120)
b1: (59, 140)
c1: (65, 146)
d1: (54, 135)
e1: (35, 116)
f1: (37, 118)
g1: (11, 92)
h1: (9, 90)
m1: (16, 97)
n2: (14, 95)
a2: (61, 142)
b2: (19, 100)
c2: (80, 161)
d2: (41, 122)
e2: (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)
f2: (71, 152)
g2: (44, 125)
h2: (28, 109)
m2: (72, 153)
n3: (17, 98)
a3: (36, 117)
b3: (68, 149)
c3: (55, 136)
d3: (34, 115)
e3: (74, 155)
f3: (25, 106)
g3: (3, 84)
h3: (63, 144)
m3: (10, 91)
n4: (76, 157)
a4: (24, 105)
b4: (23, 104)
c4: (52, 133)
d4: (20, 101)
e4: (67, 148)
f4: (49, 130)
g4: (53, 134)
h4: (2, 81)(3, 80)(4, 79)(5, 78)(6, 77)(7, 76)(8, 75)(9, 74)(10, 73)(11, 72)(12, 71)(13, 70)(14, 69)(15, 68)(16, 67)(17, 66)(18, 65)(19, 64)(20, 63)(21, 62)(22, 61)(23, 60)(24, 59)(25, 58)(26, 57)(27, 56)(28, 55)(29, 54)(30, 53)(31, 52)(32, 51)(33, 50)(34, 49)(35, 48)(36, 47)(37, 46)(38, 45)(39, 44)(40, 43)(41, 42)(83, 162)(84, 161)(85, 160)(86, 159)(87, 158)(88, 157)(89, 156)(90, 155)(91, 154)(92, 153)(93, 152)(94, 151)(95, 150)(96, 149)(97, 148)(98, 147)(99, 146)(100, 145)(101, 144)(102, 143)(103, 142)(104, 141)(105, 140)(106, 139)(107, 138)(108, 137)(109, 136)(110, 135)(111, 134)(112, 133)(113, 132)(114, 131)(115, 130)(116, 129)(117, 128)(118, 127)(119, 126)(120, 125)(121, 124)(122, 123)
m4: (33, 114)
n5: (66, 147)
a5: (60, 141)
b5: (18, 99)
c5: (70, 151)
d5: (12, 93)
e5: (5, 86)
f5: (56, 137)
g5: (38, 119)
h5: (50, 131)
m5: (31, 112)
n6: (13, 94)
a6: (57, 138)
b6: (62, 143)
c6: (58, 139)
d6: (2, 83)
e6: (21, 102)
f6: (7, 88)
g6: (6, 87)
h6: (47, 128)
m6: (64, 145)
n7: (48, 129)
a7: (45, 126)
b7: (42, 123)
c7: (27, 108)
d7: (77, 158)
e7: (43, 124)
f7: (81, 162)
g7: (4, 85)
h7: (46, 127)
m7: (75, 156)
n8: (8, 89)
a8: (51, 132)

(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.

**************

&Graph
C4[ 162, 1 ]
162
-1 2 81 83 162
-2 1 3 82 84
-3 2 4 83 85
-4 3 5 84 86
-5 4 6 85 87
-6 88 5 7 86
-7 89 6 8 87
-8 88 90 7 9
-9 89 91 8 10
-10 11 90 92 9
-11 12 91 93 10
-12 11 13 92 94
-13 12 14 93 95
-14 13 15 94 96
-15 14 16 95 97
-16 15 17 96 98
-17 99 16 18 97
-18 100 17 19 98
-19 99 101 18 20
-20 100 102 19 21
-21 22 101 103 20
-22 23 102 104 21
-23 22 24 103 105
-24 23 25 104 106
-25 24 26 105 107
-26 25 27 106 108
-27 26 28 107 109
-28 110 27 29 108
-29 111 28 30 109
-30 110 112 29 31
-31 111 113 30 32
-32 33 112 114 31
-33 34 113 115 32
-34 33 35 114 116
-35 34 36 115 117
-36 35 37 116 118
-37 36 38 117 119
-38 37 39 118 120
-39 121 38 40 119
-40 122 39 41 120
-41 121 123 40 42
-42 122 124 41 43
-43 44 123 125 42
-44 45 124 126 43
-45 44 46 125 127
-46 45 47 126 128
-47 46 48 127 129
-48 47 49 128 130
-49 48 50 129 131
-50 132 49 51 130
-51 133 50 52 131
-52 132 134 51 53
-53 133 135 52 54
-54 55 134 136 53
-55 56 135 137 54
-56 55 57 136 138
-57 56 58 137 139
-58 57 59 138 140
-59 58 60 139 141
-60 59 61 140 142
-61 143 60 62 141
-62 144 61 63 142
-63 143 145 62 64
-64 144 146 63 65
-65 66 145 147 64
-66 67 146 148 65
-67 66 68 147 149
-68 67 69 148 150
-69 68 70 149 151
-70 69 71 150 152
-71 70 72 151 153
-72 154 71 73 152
-73 155 72 74 153
-74 154 156 73 75
-75 155 157 74 76
-76 77 156 158 75
-77 78 157 159 76
-78 77 79 158 160
-79 78 80 159 161
-80 79 81 160 162
-81 1 80 82 161
-82 2 81 83 162
-83 1 3 82 84
-84 2 4 83 85
-85 3 5 84 86
-86 4 6 85 87
-87 88 5 7 86
-88 89 6 8 87
-89 88 90 7 9
-90 89 91 8 10
-91 11 90 92 9
-92 12 91 93 10
-93 11 13 92 94
-94 12 14 93 95
-95 13 15 94 96
-96 14 16 95 97
-97 15 17 96 98
-98 99 16 18 97
-99 100 17 19 98
-100 99 101 18 20
-101 100 102 19 21
-102 22 101 103 20
-103 23 102 104 21
-104 22 24 103 105
-105 23 25 104 106
-106 24 26 105 107
-107 25 27 106 108
-108 26 28 107 109
-109 110 27 29 108
-110 111 28 30 109
-111 110 112 29 31
-112 111 113 30 32
-113 33 112 114 31
-114 34 113 115 32
-115 33 35 114 116
-116 34 36 115 117
-117 35 37 116 118
-118 36 38 117 119
-119 37 39 118 120
-120 121 38 40 119
-121 122 39 41 120
-122 121 123 40 42
-123 122 124 41 43
-124 44 123 125 42
-125 45 124 126 43
-126 44 46 125 127
-127 45 47 126 128
-128 46 48 127 129
-129 47 49 128 130
-130 48 50 129 131
-131 132 49 51 130
-132 133 50 52 131
-133 132 134 51 53
-134 133 135 52 54
-135 55 134 136 53
-136 56 135 137 54
-137 55 57 136 138
-138 56 58 137 139
-139 57 59 138 140
-140 58 60 139 141
-141 59 61 140 142
-142 143 60 62 141
-143 144 61 63 142
-144 143 145 62 64
-145 144 146 63 65
-146 66 145 147 64
-147 67 146 148 65
-148 66 68 147 149
-149 67 69 148 150
-150 68 70 149 151
-151 69 71 150 152
-152 70 72 151 153
-153 154 71 73 152
-154 155 72 74 153
-155 154 156 73 75
-156 155 157 74 76
-157 77 156 158 75
-158 78 157 159 76
-159 77 79 158 160
-160 78 80 159 161
-161 79 81 160 162
-162 1 80 82 161
0

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