[Home] [Table] [Glossary] [Families]

On this page are computer-accessible forms for the graph C4[ 78, 4 ] = PS(6,13;3).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {52, 53} under the group generated by the following permutations:

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

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

**************