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On this page are computer-accessible forms for the graph C4[ 80, 3 ] = C_80(1,31).

(I) Following is a form readable by MAGMA:

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

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

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