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

On this page are computer-accessible forms for the graph C4[ 72, 24 ] = SDD(W(9,2)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {33, 61} under the group generated by the following permutations:

a: (23, 26)(27, 29)(57, 58)(59, 60)(65, 68)(66, 67)
b: (11, 14)(16, 20)(47, 50)(51, 53)(57, 60)(58, 59)
c: (6, 15)
d: (17, 21)(22, 25)(52, 54)(55, 56)(61, 64)(62, 63)
e: (1, 2)(3, 5)(4, 7)(6, 9)(8, 12)(10, 15)(11, 17)(13, 19)(14, 21)(16, 22)(18, 24)(20, 25)(23, 28)(26, 30)(27, 31)(29, 33)(38, 40)(39, 42)(41, 45)(44, 49)(46, 48)(47, 52)(50, 54)(51, 55)(53, 56)(57, 61)(58, 62)(59, 63)(60, 64)(65, 69)(66, 70)(67, 71)(68, 72)
f: (28, 30)(31, 33)(61, 62)(63, 64)(69, 72)(70, 71)
g: (26, 27)
h: (30, 31)
m: (4, 6)(15, 19)(39, 41)(44, 48)(47, 53)(50, 51)
n1: (2, 3)(12, 18)(37, 38)(40, 43)(42, 49)(45, 46)
a1: (9, 10)
b1: (7, 9)(10, 13)(42, 45)(46, 49)(52, 56)(54, 55)
c1: (34, 35)
d1: (2, 4)(3, 6)(7, 11)(9, 14)(10, 16)(12, 15)(13, 20)(17, 23)(18, 19)(21, 26)(22, 27)(25, 29)(28, 32)(30, 34)(31, 35)(33, 36)(37, 39)(38, 41)(40, 44)(42, 47)(43, 48)(45, 50)(46, 51)(49, 53)(52, 57)(54, 58)(55, 59)(56, 60)(61, 65)(62, 66)(63, 67)(64, 68)(70, 72)
e1: (21, 22)
f1: (3, 12)
g1: (14, 16)
h1: (32, 34)(35, 36)(65, 66)(67, 68)(69, 70)(71, 72)
m1: (5, 8)

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

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