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

On this page are computer-accessible forms for the graph C4[ 96, 56 ] = SS[96,21].

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {60, 61} under the group generated by the following permutations:

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

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

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