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On this page are computer-accessible forms for the graph C4[ 84, 10 ] = MC3(6,14,1,3,3,0,1).

(I) Following is a form readable by MAGMA:

g:=Graph<84|{ {1, 15}, {65, 79}, {64, 78}, {49, 63}, {48, 62}, {17, 31}, {16, 30}, {32, 46}, {33, 47}, {2, 16}, {70, 84}, {67, 81}, {66, 80}, {47, 61}, {46, 60}, {43, 57}, {42, 56}, {39, 53}, {38, 52}, {35, 49}, {34, 48}, {15, 29}, {14, 28}, {11, 25}, {10, 24}, {7, 21}, {6, 20}, {3, 17}, {4, 18}, {69, 83}, {68, 82}, {45, 59}, {44, 58}, {37, 51}, {36, 50}, {13, 27}, {12, 26}, {5, 19}, {8, 22}, {41, 55}, {40, 54}, {9, 23}, {13, 44}, {27, 58}, {14, 45}, {26, 57}, {14, 43}, {24, 61}, {26, 63}, {12, 43}, {25, 62}, {28, 59}, {4, 47}, {23, 60}, {1, 44}, {18, 63}, {16, 61}, {3, 46}, {2, 47}, {20, 57}, {22, 59}, {1, 46}, {17, 62}, {2, 45}, {21, 58}, {18, 32}, {19, 33}, {22, 36}, {23, 37}, {26, 40}, {27, 41}, {30, 44}, {31, 45}, {3, 48}, {15, 60}, {11, 56}, {7, 52}, {4, 49}, {13, 56}, {7, 50}, {6, 51}, {5, 48}, {20, 34}, {21, 35}, {28, 42}, {29, 43}, {5, 50}, {6, 49}, {8, 51}, {12, 55}, {8, 53}, {11, 54}, {10, 55}, {9, 52}, {24, 38}, {25, 39}, {9, 54}, {10, 53}, {1, 71}, {9, 79}, {8, 78}, {29, 84}, {2, 72}, {7, 77}, {6, 76}, {3, 73}, {15, 66}, {29, 80}, {31, 82}, {4, 74}, {5, 75}, {30, 81}, {16, 67}, {19, 64}, {23, 68}, {17, 68}, {19, 70}, {20, 65}, {22, 67}, {18, 69}, {21, 66}, {31, 72}, {30, 71}, {10, 80}, {14, 84}, {11, 81}, {27, 64}, {24, 69}, {28, 65}, {12, 82}, {13, 83}, {25, 70}, {34, 71}, {42, 79}, {40, 77}, {41, 78}, {32, 73}, {38, 79}, {36, 77}, {34, 75}, {33, 74}, {39, 76}, {37, 78}, {35, 72}, {36, 73}, {38, 75}, {35, 76}, {37, 74}, {50, 64}, {63, 77}, {62, 76}, {59, 73}, {58, 72}, {55, 69}, {54, 68}, {51, 65}, {32, 83}, {33, 84}, {52, 66}, {61, 75}, {60, 74}, {53, 67}, {39, 80}, {40, 81}, {42, 83}, {41, 82}, {56, 70}, {57, 71} }>;

(II) A more general form is to represent the graph as the orbit of {1, 15} under the group generated by the following permutations:

a: (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, 81, 82, 83, 84)
b: (2, 9)(3, 34)(4, 40)(5, 62)(6, 36)(7, 35)(10, 41)(11, 33)(12, 69)(13, 29)(14, 42)(15, 44)(16, 23)(17, 75)(18, 26)(19, 25)(20, 73)(22, 51)(24, 82)(27, 80)(30, 60)(31, 38)(32, 57)(37, 67)(39, 64)(43, 83)(45, 79)(46, 71)(47, 54)(49, 77)(50, 76)(52, 72)(53, 78)(56, 84)(58, 66)(59, 65)(61, 68)(74, 81)
c: (2, 4, 61, 33)(3, 57, 66, 13)(5, 14, 35, 69)(6, 10, 64, 59)(7, 42, 62, 12)(9, 11, 68, 40)(15, 44, 46, 71)(16, 74)(17, 26, 52, 56)(18, 75, 84, 72)(19, 45, 49, 24)(20, 80, 27, 73)(21, 83, 48, 43)(22, 51, 53, 78)(23, 81)(25, 82, 77, 79)(28, 76, 55, 50)(29, 58, 32, 34)(30, 60)(31, 63, 38, 70)(36, 65, 39, 41)(37, 67)
d: (1, 15, 29, 43, 57, 71)(2, 18, 38, 56, 68, 76)(3, 21, 33, 55, 65, 81)(4, 24, 42, 54, 62, 72)(5, 27, 37, 53, 59, 77)(6, 16, 32, 52, 70, 82)(7, 19, 41, 51, 67, 73)(8, 22, 36, 50, 64, 78)(9, 25, 31, 49, 61, 83)(10, 28, 40, 48, 58, 74)(11, 17, 35, 47, 69, 79)(12, 20, 30, 46, 66, 84)(13, 23, 39, 45, 63, 75)(14, 26, 34, 44, 60, 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[ 84, 10 ]
84
-1 44 46 15 71
-2 45 47 16 72
-3 46 48 17 73
-4 47 49 18 74
-5 48 50 19 75
-6 49 51 20 76
-7 77 50 52 21
-8 22 78 51 53
-9 23 79 52 54
-10 55 24 80 53
-11 56 25 81 54
-12 55 26 82 43
-13 44 56 27 83
-14 45 28 84 43
-15 66 1 60 29
-16 67 2 61 30
-17 68 3 62 31
-18 69 4 63 32
-19 33 70 5 64
-20 34 57 6 65
-21 66 35 58 7
-22 67 36 59 8
-23 68 37 60 9
-24 69 38 61 10
-25 11 70 39 62
-26 12 57 40 63
-27 13 58 41 64
-28 14 59 42 65
-29 80 15 84 43
-30 44 81 16 71
-31 45 82 17 72
-32 46 83 18 73
-33 47 84 19 74
-34 48 71 20 75
-35 49 72 21 76
-36 22 77 50 73
-37 23 78 51 74
-38 24 79 52 75
-39 25 80 53 76
-40 77 26 81 54
-41 55 78 27 82
-42 56 79 28 83
-43 12 57 14 29
-44 1 13 58 30
-45 2 14 59 31
-46 1 3 60 32
-47 33 2 4 61
-48 34 3 5 62
-49 35 4 6 63
-50 36 5 7 64
-51 37 6 8 65
-52 66 38 7 9
-53 67 39 8 10
-54 11 68 40 9
-55 12 69 41 10
-56 11 13 70 42
-57 26 71 20 43
-58 44 27 72 21
-59 22 45 28 73
-60 23 46 15 74
-61 24 47 16 75
-62 25 48 17 76
-63 77 26 49 18
-64 78 27 50 19
-65 79 28 51 20
-66 80 15 52 21
-67 22 81 16 53
-68 23 82 17 54
-69 55 24 83 18
-70 56 25 84 19
-71 1 34 57 30
-72 2 35 58 31
-73 3 36 59 32
-74 33 4 37 60
-75 34 5 38 61
-76 35 6 39 62
-77 36 7 40 63
-78 37 8 41 64
-79 38 9 42 65
-80 66 39 29 10
-81 11 67 40 30
-82 12 68 41 31
-83 13 69 42 32
-84 33 14 70 29
0

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