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On this page are computer-accessible forms for the graph C4[ 84, 15 ] = UG(ATD[84,21]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {74, 75} under the group generated by the following permutations:

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

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

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