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On this page are computer-accessible forms for the graph C4[ 80, 17 ] = KE_20(1,7,2,15,1).

(I) Following is a form readable by MAGMA:

g:=Graph<80|{ {2, 3}, {78, 79}, {76, 77}, {74, 75}, {72, 73}, {70, 71}, {68, 69}, {66, 67}, {64, 65}, {62, 63}, {18, 19}, {16, 17}, {14, 15}, {12, 13}, {10, 11}, {8, 9}, {6, 7}, {4, 5}, {40, 42}, {1, 2}, {77, 78}, {73, 74}, {69, 70}, {65, 66}, {61, 62}, {17, 18}, {13, 14}, {9, 10}, {5, 6}, {3, 4}, {75, 76}, {67, 68}, {19, 20}, {11, 12}, {16, 29}, {18, 31}, {39, 41}, {7, 8}, {71, 72}, {17, 30}, {11, 24}, {15, 28}, {32, 52}, {43, 63}, {42, 62}, {41, 61}, {33, 53}, {34, 54}, {35, 55}, {40, 60}, {1, 20}, {14, 27}, {12, 25}, {32, 54}, {33, 55}, {13, 26}, {34, 56}, {35, 57}, {38, 60}, {36, 56}, {37, 57}, {38, 58}, {39, 59}, {8, 21}, {10, 23}, {36, 58}, {37, 59}, {9, 22}, {79, 80}, {15, 16}, {2, 35}, {6, 39}, {4, 37}, {1, 34}, {5, 38}, {28, 63}, {27, 62}, {3, 36}, {26, 61}, {1, 41}, {20, 60}, {19, 59}, {18, 58}, {17, 57}, {16, 56}, {7, 47}, {6, 46}, {5, 45}, {4, 44}, {3, 43}, {2, 42}, {26, 48}, {27, 49}, {30, 52}, {31, 53}, {28, 48}, {29, 49}, {30, 50}, {31, 51}, {28, 50}, {29, 51}, {7, 40}, {19, 32}, {24, 44}, {25, 45}, {26, 46}, {27, 47}, {20, 33}, {24, 46}, {25, 47}, {8, 48}, {15, 55}, {14, 54}, {13, 53}, {12, 52}, {11, 51}, {10, 50}, {9, 49}, {22, 44}, {23, 45}, {21, 41}, {22, 42}, {23, 43}, {21, 43}, {25, 80}, {24, 79}, {21, 76}, {23, 78}, {22, 77}, {29, 64}, {31, 66}, {30, 65}, {32, 67}, {40, 75}, {36, 71}, {33, 68}, {35, 70}, {34, 69}, {44, 64}, {60, 80}, {47, 67}, {46, 66}, {45, 65}, {37, 72}, {61, 80}, {39, 74}, {38, 73}, {48, 68}, {59, 79}, {58, 78}, {57, 77}, {56, 76}, {51, 71}, {50, 70}, {49, 69}, {52, 72}, {55, 75}, {54, 74}, {53, 73}, {63, 64} }>;

(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, 34, 20, 41)(3, 69, 19, 61)(4, 49, 18, 26)(5, 9, 17, 13)(6, 22, 16, 53)(7, 77, 15, 73)(8, 57, 14, 38)(10, 30, 12, 45)(11, 65)(21, 35, 54, 60)(23, 50, 52, 25)(24, 64, 51, 66)(27, 58, 48, 37)(28, 72, 47, 78)(29, 31, 46, 44)(32, 80, 43, 70)(33, 39, 42, 56)(36, 68, 59, 62)(40, 76, 55, 74)(63, 71, 67, 79)
b: (2, 20)(3, 19)(4, 18)(5, 17)(6, 16)(7, 15)(8, 14)(9, 13)(10, 12)(21, 54)(22, 53)(23, 52)(24, 51)(25, 50)(26, 49)(27, 48)(28, 47)(29, 46)(30, 45)(31, 44)(32, 43)(33, 42)(34, 41)(35, 60)(36, 59)(37, 58)(38, 57)(39, 56)(40, 55)(61, 69)(62, 68)(63, 67)(64, 66)(70, 80)(71, 79)(72, 78)(73, 77)(74, 76)
c: (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)

(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[ 80, 17 ]
80
-1 34 2 41 20
-2 1 35 3 42
-3 2 36 4 43
-4 44 3 37 5
-5 45 4 38 6
-6 46 5 39 7
-7 47 6 40 8
-8 48 7 9 21
-9 22 49 8 10
-10 11 23 50 9
-11 12 24 51 10
-12 11 13 25 52
-13 12 14 26 53
-14 13 15 27 54
-15 55 14 16 28
-16 56 15 17 29
-17 57 16 18 30
-18 58 17 19 31
-19 59 18 20 32
-20 33 1 60 19
-21 8 41 43 76
-22 44 77 9 42
-23 45 78 10 43
-24 11 44 46 79
-25 12 45 47 80
-26 13 46 48 61
-27 14 47 49 62
-28 15 48 50 63
-29 16 49 51 64
-30 17 50 52 65
-31 66 18 51 53
-32 67 19 52 54
-33 55 68 20 53
-34 1 56 69 54
-35 55 2 57 70
-36 56 3 58 71
-37 57 4 59 72
-38 58 5 60 73
-39 59 6 41 74
-40 60 7 42 75
-41 1 39 61 21
-42 22 2 40 62
-43 23 3 63 21
-44 22 24 4 64
-45 23 25 5 65
-46 66 24 26 6
-47 67 25 27 7
-48 68 26 28 8
-49 69 27 29 9
-50 70 28 30 10
-51 11 71 29 31
-52 12 72 30 32
-53 33 13 73 31
-54 34 14 74 32
-55 33 35 15 75
-56 34 36 16 76
-57 77 35 37 17
-58 78 36 38 18
-59 79 37 39 19
-60 80 38 40 20
-61 80 26 62 41
-62 27 61 63 42
-63 28 62 64 43
-64 44 29 63 65
-65 66 45 30 64
-66 67 46 31 65
-67 66 68 47 32
-68 33 67 69 48
-69 34 68 70 49
-70 35 69 71 50
-71 36 70 72 51
-72 37 71 73 52
-73 38 72 74 53
-74 39 73 75 54
-75 55 40 74 76
-76 77 56 75 21
-77 22 78 57 76
-78 77 23 79 58
-79 78 24 80 59
-80 79 25 60 61
0

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