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On this page are computer-accessible forms for the graph C4[ 84, 1 ] = W(42, 2).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {2, 3} under the group generated by the following permutations:

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

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

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