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On this page are computer-accessible forms for the graph C4[ 80, 5 ] = {4,4}_[10,4].

(I) Following is a form readable by MAGMA:

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

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