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

On this page are computer-accessible forms for the graph C4[ 100, 10 ] = BGCG(K5,K55).

(I) Following is a form readable by MAGMA:

g:=Graph<100|{ {50, 54}, {49, 56}, {36, 52}, {38, 52}, {32, 51}, {40, 60}, {47, 56}, {35, 59}, {46, 54}, {39, 63}, {44, 53}, {33, 59}, {36, 63}, {39, 60}, {41, 53}, {43, 55}, {42, 55}, {33, 62}, {31, 62}, {27, 57}, {27, 61}, {28, 58}, {26, 61}, {29, 58}, {30, 57}, {31, 51}, {2, 51}, {4, 53}, {1, 51}, {5, 54}, {1, 53}, {3, 55}, {1, 52}, {2, 55}, {8, 62}, {9, 63}, {1, 54}, {3, 52}, {3, 59}, {6, 62}, {4, 60}, {3, 58}, {6, 63}, {5, 60}, {2, 56}, {7, 61}, {2, 57}, {6, 61}, {4, 56}, {5, 57}, {4, 58}, {5, 59}, {12, 76}, {34, 98}, {18, 82}, {17, 81}, {15, 79}, {14, 78}, {19, 83}, {20, 84}, {30, 94}, {11, 74}, {32, 97}, {16, 81}, {12, 77}, {11, 73}, {35, 97}, {16, 82}, {15, 77}, {14, 76}, {13, 79}, {11, 72}, {33, 98}, {16, 83}, {13, 78}, {20, 87}, {7, 67}, {17, 85}, {16, 84}, {26, 94}, {7, 66}, {38, 99}, {15, 74}, {13, 72}, {19, 86}, {24, 93}, {6, 64}, {17, 87}, {13, 75}, {7, 65}, {12, 75}, {18, 85}, {17, 86}, {14, 73}, {25, 94}, {21, 93}, {44, 100}, {23, 95}, {8, 65}, {45, 100}, {10, 67}, {19, 90}, {21, 92}, {22, 95}, {26, 83}, {28, 85}, {10, 64}, {18, 88}, {9, 66}, {40, 99}, {12, 71}, {18, 89}, {19, 88}, {21, 94}, {23, 92}, {31, 84}, {8, 68}, {11, 71}, {10, 70}, {8, 69}, {9, 68}, {20, 89}, {22, 91}, {29, 80}, {20, 90}, {21, 91}, {27, 85}, {29, 83}, {30, 80}, {9, 70}, {10, 69}, {26, 72}, {28, 72}, {31, 73}, {28, 69}, {30, 69}, {14, 80}, {15, 80}, {45, 77}, {40, 74}, {48, 82}, {44, 78}, {34, 70}, {37, 65}, {35, 70}, {43, 78}, {38, 65}, {42, 77}, {42, 66}, {50, 90}, {47, 71}, {37, 76}, {46, 71}, {41, 64}, {33, 75}, {32, 75}, {49, 90}, {39, 76}, {34, 73}, {47, 67}, {49, 93}, {45, 64}, {36, 74}, {44, 66}, {48, 95}, {47, 95}, {50, 67}, {37, 87}, {43, 89}, {46, 93}, {23, 99}, {48, 68}, {45, 89}, {34, 86}, {23, 98}, {49, 68}, {41, 92}, {22, 96}, {32, 86}, {22, 97}, {43, 92}, {35, 84}, {24, 96}, {41, 81}, {25, 97}, {24, 98}, {25, 99}, {27, 96}, {42, 81}, {24, 100}, {46, 82}, {25, 100}, {50, 79}, {29, 96}, {37, 91}, {38, 88}, {36, 91}, {48, 79}, {40, 87}, {39, 88} }>;

(II) A more general form is to represent the graph as the orbit of {50, 54} under the group generated by the following permutations:

a: (2, 5)(3, 4)(6, 7)(8, 10)(11, 13)(14, 15)(16, 19)(17, 18)(21, 25)(22, 24)(31, 50)(32, 46)(33, 47)(34, 48)(35, 49)(36, 44)(37, 45)(38, 41)(39, 42)(40, 43)(51, 54)(52, 53)(55, 60)(56, 59)(62, 67)(63, 66)(64, 65)(68, 70)(71, 75)(73, 79)(74, 78)(76, 77)(81, 88)(82, 86)(84, 90)(87, 89)(91, 100)(92, 99)(93, 97)(95, 98)
b: (1, 26)(2, 30)(3, 29)(4, 28)(5, 27)(6, 46)(7, 50)(8, 49)(9, 48)(10, 47)(11, 41)(12, 45)(13, 44)(14, 43)(15, 42)(16, 36)(17, 40)(18, 39)(19, 38)(20, 37)(21, 31)(22, 35)(23, 34)(24, 33)(25, 32)(51, 94)(52, 83)(53, 72)(54, 61)(55, 80)(56, 69)(59, 96)(60, 85)(62, 93)(63, 82)(64, 71)(65, 90)(66, 79)(70, 95)(73, 92)(74, 81)(75, 100)(76, 89)(84, 91)(86, 99)
c: (1, 6, 5, 10, 4, 9, 3, 8, 2, 7)(11, 24, 15, 23, 14, 22, 13, 21, 12, 25)(16, 18, 20, 17, 19)(26, 46, 45, 40, 34, 29, 48, 43, 37, 32)(27, 50, 41, 39, 35, 28, 49, 42, 38, 31)(30, 47, 44, 36, 33)(51, 61, 54, 64, 60, 70, 58, 68, 55, 65)(52, 62, 57, 67, 53, 63, 59, 69, 56, 66)(71, 100, 74, 98, 80, 95, 78, 91, 75, 94)(72, 93, 77, 99, 73, 96, 79, 92, 76, 97)(81, 88, 84, 85, 90)(82, 89, 87, 86, 83)
d: (1, 2)(3, 5)(6, 8)(9, 10)(11, 14)(12, 13)(16, 20)(17, 19)(22, 25)(23, 24)(26, 37)(27, 38)(28, 39)(29, 40)(30, 36)(41, 49)(42, 50)(43, 46)(44, 47)(45, 48)(52, 57)(53, 56)(54, 55)(58, 60)(61, 65)(63, 69)(64, 68)(66, 67)(71, 78)(72, 76)(74, 80)(77, 79)(81, 90)(82, 89)(83, 87)(85, 88)(91, 94)(92, 93)(95, 100)(96, 99)
e: (2, 4, 5, 3)(6, 13, 21, 19)(7, 11, 25, 16)(8, 14, 24, 18)(9, 12, 23, 20)(10, 15, 22, 17)(27, 28, 30, 29)(31, 44, 46, 38)(32, 41, 50, 36)(33, 43, 49, 39)(34, 45, 48, 37)(35, 42, 47, 40)(51, 53, 54, 52)(55, 56, 60, 59)(57, 58)(61, 72, 94, 83)(62, 78, 93, 88)(63, 75, 92, 90)(64, 79, 91, 86)(65, 73, 100, 82)(66, 71, 99, 84)(67, 74, 97, 81)(68, 76, 98, 89)(69, 80, 96, 85)(70, 77, 95, 87)

(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[ 100, 10 ]
100
-1 51 52 53 54
-2 55 56 57 51
-3 55 58 59 52
-4 56 58 60 53
-5 57 59 60 54
-6 61 62 63 64
-7 66 67 61 65
-8 68 69 62 65
-9 66 68 70 63
-10 67 69 70 64
-11 71 72 73 74
-12 77 71 75 76
-13 78 79 72 75
-14 78 80 73 76
-15 77 79 80 74
-16 81 82 83 84
-17 81 85 86 87
-18 88 89 82 85
-19 88 90 83 86
-20 89 90 84 87
-21 91 92 93 94
-22 91 95 96 97
-23 99 92 95 98
-24 100 93 96 98
-25 99 100 94 97
-26 72 94 61 83
-27 57 61 85 96
-28 58 69 72 85
-29 58 80 83 96
-30 57 69 80 94
-31 51 73 62 84
-32 51 75 86 97
-33 59 62 75 98
-34 70 73 86 98
-35 59 70 84 97
-36 91 52 63 74
-37 91 65 76 87
-38 88 99 52 65
-39 88 60 63 76
-40 99 60 74 87
-41 81 92 53 64
-42 55 66 77 81
-43 55 78 89 92
-44 66 78 100 53
-45 77 89 100 64
-46 71 82 93 54
-47 56 67 71 95
-48 68 79 82 95
-49 56 68 90 93
-50 67 79 90 54
-51 1 2 31 32
-52 1 3 36 38
-53 44 1 4 41
-54 1 46 5 50
-55 2 3 42 43
-56 2 47 4 49
-57 2 5 27 30
-58 3 4 28 29
-59 33 35 3 5
-60 4 5 39 40
-61 26 27 6 7
-62 33 6 8 31
-63 36 6 39 9
-64 45 6 41 10
-65 37 38 7 8
-66 44 7 9 42
-67 47 50 7 10
-68 48 49 8 9
-69 28 8 30 10
-70 34 35 9 10
-71 11 12 46 47
-72 11 13 26 28
-73 11 34 14 31
-74 11 36 15 40
-75 33 12 13 32
-76 12 14 37 39
-77 12 45 15 42
-78 44 13 14 43
-79 13 15 48 50
-80 14 15 29 30
-81 16 17 41 42
-82 46 48 16 18
-83 26 16 29 19
-84 35 16 20 31
-85 27 17 28 18
-86 34 17 19 32
-87 37 17 40 20
-88 38 39 18 19
-89 45 18 20 43
-90 49 50 19 20
-91 22 36 37 21
-92 23 41 21 43
-93 24 46 49 21
-94 25 26 30 21
-95 22 23 47 48
-96 22 24 27 29
-97 22 35 25 32
-98 33 23 34 24
-99 23 25 38 40
-100 44 45 24 25
0

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