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On this page are computer-accessible forms for the graph C4[ 84, 16 ] = UG(ATD[84,22]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {20, 21} under the group generated by the following permutations:

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

**************

&Graph
C4[ 84, 16 ]
84
-1 2 13 3 21
-2 22 1 4 5
-3 1 6 8 30
-4 2 7 9 31
-5 2 13 16 10
-6 11 3 14 43
-7 44 12 4 15
-8 3 16 10 21
-9 22 25 4 17
-10 58 5 18 8
-11 23 59 6 19
-12 24 60 7 20
-13 1 25 5 17
-14 35 6 30 20
-15 36 26 7 31
-16 5 27 49 8
-17 13 28 19 9
-18 29 73 10 32
-19 11 33 45 17
-20 12 34 14 21
-21 1 35 8 20
-22 2 36 26 9
-23 11 47 37 43
-24 44 12 48 38
-25 13 39 9 65
-26 22 15 29 40
-27 16 84 41 32
-28 77 45 17 42
-29 46 26 61 18
-30 3 14 47 37
-31 4 15 48 38
-32 58 27 49 18
-33 59 50 19 63
-34 60 51 20 64
-35 78 14 52 21
-36 22 79 15 53
-37 23 30 41 54
-38 55 24 31 42
-39 45 56 25 83
-40 57 26 61 63
-41 37 27 62 74
-42 59 38 71 28
-43 23 6 50 63
-44 24 7 51 64
-45 28 39 19 65
-46 66 29 73 76
-47 23 67 79 30
-48 24 84 31 54
-49 56 68 16 32
-50 33 69 51 43
-51 44 34 57 50
-52 66 35 60 72
-53 36 70 82 61
-54 37 48 71 74
-55 38 71 72 76
-56 49 39 62 75
-57 69 40 51 73
-58 66 10 32 76
-59 11 33 77 42
-60 12 34 78 52
-61 79 29 40 53
-62 56 68 84 41
-63 33 40 73 43
-64 44 34 68 83
-65 45 25 80 70
-66 46 58 81 52
-67 47 70 82 74
-68 69 49 62 64
-69 57 68 50 83
-70 67 53 75 65
-71 55 84 42 54
-72 55 77 81 52
-73 46 57 18 63
-74 67 79 41 54
-75 56 80 70 83
-76 55 77 46 58
-77 59 28 72 76
-78 35 80 60 82
-79 36 47 61 74
-80 78 81 75 65
-81 66 80 82 72
-82 67 78 81 53
-83 69 39 64 75
-84 48 27 71 62
0

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