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On this page are computer-accessible forms for the graph C4[ 84, 4 ] = {4,4}_<10,4>.

(I) Following is a form readable by MAGMA:

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

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

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

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