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On this page are computer-accessible forms for the graph C4[ 84, 11 ] = MC3(6,14,1,10,3,0,1).

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

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

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