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On this page are computer-accessible forms for the graph C4[ 81, 7 ] = UG(ATD[81,12]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {21, 23} under the group generated by the following permutations:

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

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

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