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On this page are computer-accessible forms for the graph C4[ 80, 19 ] = KE_20(1,11,3,7,6).

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

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

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

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