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On this page are computer-accessible forms for the graph C4[ 160, 39 ] = KE_40(1,21,8,17,11).

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

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

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