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On this page are computer-accessible forms for the graph C4[ 160, 41 ] = KE_40(1,25,18,13,19).

(I) Following is a form readable by MAGMA:

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

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

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

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