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

On this page are computer-accessible forms for the graph C4[ 81, 7 ] = MCA[ 81, 4 ].

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {74, 75} under the group generated by the following permutations:

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

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

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