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On this page are computer-accessible forms for the graph C4[ 81, 6 ] = AMC(9,3,[0.1:2.2]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {54, 55} under the group generated by the following permutations:

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

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

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