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On this page are computer-accessible forms for the graph C4[ 80, 4 ] = {4,4}_8,4.

(I) Following is a form readable by MAGMA:

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

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