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On this page are computer-accessible forms for the graph C4[ 84, 12 ] = MC3(6,14,1,12,3,0,1).

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

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