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On this page are computer-accessible forms for the graph C4[ 80, 18 ] = KE_20(1,9,7,13,4).

(I) Following is a form readable by MAGMA:

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

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

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&Graph
C4[ 80, 18 ]
80
-1 2 41 20 32
-2 33 1 3 42
-3 34 2 4 43
-4 44 35 3 5
-5 45 36 4 6
-6 46 37 5 7
-7 47 38 6 8
-8 48 39 7 9
-9 49 40 8 10
-10 11 50 9 21
-11 22 12 51 10
-12 11 23 13 52
-13 12 24 14 53
-14 13 25 15 54
-15 55 14 26 16
-16 56 15 27 17
-17 57 16 28 18
-18 58 17 29 19
-19 59 18 30 20
-20 1 60 19 31
-21 48 41 74 10
-22 11 49 42 75
-23 12 50 43 76
-24 44 77 13 51
-25 45 78 14 52
-26 46 79 15 53
-27 47 80 16 54
-28 55 48 17 61
-29 56 49 18 62
-30 57 50 19 63
-31 58 51 20 64
-32 1 59 52 65
-33 66 2 60 53
-34 67 3 41 54
-35 55 68 4 42
-36 56 69 5 43
-37 44 57 70 6
-38 45 58 71 7
-39 46 59 72 8
-40 47 60 73 9
-41 1 34 61 21
-42 22 2 35 62
-43 23 3 36 63
-44 24 4 37 64
-45 25 5 38 65
-46 66 26 6 39
-47 67 27 7 40
-48 68 28 8 21
-49 22 69 29 9
-50 23 70 30 10
-51 11 24 71 31
-52 12 25 72 32
-53 33 13 26 73
-54 34 14 27 74
-55 35 15 28 75
-56 36 16 29 76
-57 77 37 17 30
-58 78 38 18 31
-59 79 39 19 32
-60 33 80 40 20
-61 77 28 41 65
-62 66 78 29 42
-63 67 79 30 43
-64 44 68 80 31
-65 45 69 61 32
-66 33 46 70 62
-67 34 47 71 63
-68 35 48 72 64
-69 36 49 73 65
-70 66 37 50 74
-71 67 38 51 75
-72 68 39 52 76
-73 77 69 40 53
-74 78 70 21 54
-75 22 55 79 71
-76 23 56 80 72
-77 24 57 61 73
-78 25 58 62 74
-79 26 59 63 75
-80 27 60 64 76
0

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