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On this page are computer-accessible forms for the graph C4[ 84, 13 ] = Pr_28(1,5,9,13).

(I) Following is a form readable by MAGMA:

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

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

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