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On this page are computer-accessible forms for the graph C4[ 84, 3 ] = C_84(1,29).

(I) Following is a form readable by MAGMA:

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

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

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

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