Graph forms for C4 [ 108, 24 ] = SDD(AMC(3,3,[0.1:2.2]))

On this page are computer-accessible forms for the graph C4[ 108, 24 ] = SDD(AMC(3,3,[0.1:2.2])).

(I) Following is a form readable by MAGMA:

g:=Graph<108|{ {38, 61}, {20, 55}, {26, 62}, {28, 58}, {19, 56}, {20, 56}, {18, 63}, {20, 57}, {19, 61}, {20, 59}, {11, 59}, {12, 60}, {12, 63}, {2, 55}, {10, 63}, {8, 61}, {1, 55}, {12, 58}, {9, 62}, {1, 57}, {4, 60}, {2, 58}, {1, 56}, {7, 62}, {1, 59}, {4, 62}, {3, 56}, {12, 55}, {7, 60}, {2, 63}, {6, 59}, {4, 57}, {2, 60}, {7, 57}, {3, 61}, {5, 58}, {5, 69}, {30, 94}, {34, 98}, {35, 99}, {15, 78}, {23, 86}, {33, 96}, {41, 104}, {10, 72}, {18, 80}, {11, 73}, {42, 104}, {3, 64}, {23, 84}, {22, 85}, {15, 76}, {14, 77}, {8, 75}, {27, 88}, {32, 99}, {34, 97}, {5, 65}, {46, 106}, {45, 105}, {7, 67}, {6, 66}, {9, 76}, {41, 108}, {6, 64}, {3, 68}, {46, 105}, {4, 67}, {37, 98}, {16, 88}, {47, 103}, {26, 82}, {17, 89}, {29, 85}, {33, 105}, {41, 97}, {11, 66}, {47, 102}, {21, 92}, {31, 85}, {46, 100}, {44, 102}, {11, 64}, {44, 103}, {24, 83}, {22, 93}, {13, 70}, {13, 65}, {15, 67}, {14, 66}, {25, 84}, {45, 96}, {40, 101}, {8, 70}, {9, 71}, {5, 74}, {25, 86}, {24, 87}, {10, 69}, {6, 73}, {39, 104}, {43, 100}, {25, 73}, {52, 100}, {27, 75}, {30, 79}, {48, 97}, {31, 78}, {17, 67}, {48, 98}, {24, 74}, {21, 71}, {19, 64}, {54, 101}, {51, 96}, {29, 78}, {16, 68}, {53, 97}, {27, 79}, {14, 91}, {50, 103}, {15, 89}, {54, 96}, {51, 101}, {26, 76}, {28, 74}, {13, 90}, {19, 68}, {18, 69}, {21, 77}, {51, 107}, {8, 81}, {53, 108}, {51, 106}, {28, 69}, {10, 80}, {18, 72}, {14, 84}, {9, 82}, {16, 75}, {54, 106}, {17, 76}, {54, 107}, {53, 104}, {52, 105}, {26, 71}, {28, 65}, {13, 83}, {52, 106}, {50, 108}, {23, 73}, {22, 72}, {16, 79}, {27, 68}, {17, 78}, {38, 70}, {40, 72}, {48, 82}, {53, 87}, {49, 83}, {36, 66}, {43, 77}, {36, 77}, {49, 90}, {43, 71}, {50, 94}, {48, 92}, {38, 75}, {37, 74}, {52, 91}, {32, 80}, {49, 65}, {33, 81}, {34, 82}, {36, 84}, {21, 100}, {39, 86}, {30, 108}, {37, 87}, {22, 101}, {35, 80}, {23, 99}, {44, 88}, {31, 107}, {42, 94}, {40, 93}, {46, 91}, {44, 89}, {42, 95}, {29, 107}, {47, 89}, {37, 83}, {38, 81}, {49, 70}, {47, 88}, {45, 90}, {43, 92}, {39, 95}, {30, 103}, {31, 102}, {39, 94}, {24, 98}, {25, 99}, {29, 102}, {33, 90}, {35, 95}, {45, 81}, {42, 86}, {32, 93}, {50, 79}, {40, 85}, {34, 92}, {35, 93}, {41, 87}, {32, 95}, {36, 91} }>;

(II) A more general form is to represent the graph as the orbit of {38, 61} under the group generated by the following permutations:

a: (41, 53)
b: (8, 38)
c: (2, 3)(4, 6)(5, 8)(7, 11)(9, 14)(10, 16)(12, 19)(15, 23)(17, 25)(18, 27)(22, 30)(24, 33)(26, 36)(28, 38)(29, 39)(31, 42)(32, 44)(34, 46)(35, 47)(37, 45)(40, 50)(41, 51)(48, 52)(53, 54)(55, 56)(57, 59)(58, 61)(60, 64)(62, 66)(63, 68)(65, 70)(67, 73)(69, 75)(71, 77)(72, 79)(74, 81)(76, 84)(78, 86)(80, 88)(82, 91)(83, 90)(85, 94)(87, 96)(89, 99)(92, 100)(93, 103)(95, 102)(97, 106)(98, 105)(101, 108)(104, 107)
d: (10, 18)
e: (4, 7)
f: (6, 11)
g: (13, 49)
h: (30, 50)
m: (34, 48)
n1: (32, 35)
a1: (1, 2)(3, 5)(6, 10)(8, 13)(9, 15)(11, 18)(12, 20)(14, 22)(16, 24)(17, 26)(19, 28)(21, 29)(23, 32)(25, 35)(27, 37)(30, 41)(31, 43)(34, 44)(36, 40)(38, 49)(46, 51)(47, 48)(50, 53)(52, 54)(56, 58)(57, 60)(59, 63)(61, 65)(62, 67)(64, 69)(66, 72)(68, 74)(71, 78)(73, 80)(75, 83)(77, 85)(79, 87)(81, 90)(82, 89)(84, 93)(86, 95)(88, 98)(91, 101)(92, 102)(94, 104)(96, 105)(97, 103)(100, 107)
b1: (3, 6)(5, 10)(8, 23)(9, 15)(11, 19)(13, 32)(14, 16)(17, 26)(18, 28)(21, 44)(22, 24)(25, 38)(27, 36)(29, 34)(30, 46)(31, 48)(33, 39)(35, 49)(37, 40)(41, 51)(42, 45)(43, 47)(50, 52)(53, 54)(56, 59)(58, 63)(61, 73)(62, 67)(65, 80)(66, 68)(70, 99)(71, 89)(72, 74)(75, 84)(77, 88)(78, 82)(79, 91)(81, 86)(83, 93)(85, 98)(87, 101)(90, 95)(92, 102)(94, 105)(96, 104)(97, 107)(100, 103)(106, 108)
c1: (39, 42)
d1: (9, 26)
e1: (23, 25)
f1: (51, 54)
g1: (14, 36)
h1: (2, 4)(3, 6)(5, 9)(7, 12)(8, 14)(10, 15)(11, 19)(13, 21)(16, 23)(17, 18)(22, 29)(24, 34)(25, 27)(26, 28)(30, 39)(31, 40)(32, 44)(33, 46)(35, 47)(36, 38)(37, 48)(42, 50)(43, 49)(45, 52)(55, 57)(56, 59)(58, 62)(61, 66)(63, 67)(65, 71)(68, 73)(69, 76)(70, 77)(72, 78)(74, 82)(75, 84)(79, 86)(80, 89)(81, 91)(83, 92)(87, 97)(88, 99)(90, 100)(93, 102)(95, 103)(96, 106)(101, 107)(104, 108)
m1: (33, 45)
n2: (16, 27)
a2: (21, 43)
b2: (15, 17)
c2: (44, 47)
d2: (46, 52)
e2: (3, 19)
f2: (5, 28)
g2: (29, 31)
h2: (24, 37)
m2: (2, 12)

(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[ 108, 24 ]
108
-1 55 56 57 59
-2 55 58 60 63
-3 56 68 61 64
-4 67 57 60 62
-5 58 69 74 65
-6 66 59 73 64
-7 67 57 60 62
-8 70 81 61 75
-9 71 82 62 76
-10 69 80 72 63
-11 66 59 73 64
-12 55 58 60 63
-13 90 70 83 65
-14 66 77 91 84
-15 67 78 89 76
-16 88 68 79 75
-17 67 78 89 76
-18 69 80 72 63
-19 56 68 61 64
-20 55 56 57 59
-21 77 100 92 71
-22 101 93 72 85
-23 99 73 84 86
-24 83 74 87 98
-25 99 73 84 86
-26 71 82 62 76
-27 88 68 79 75
-28 58 69 74 65
-29 78 102 85 107
-30 79 103 94 108
-31 78 102 85 107
-32 99 80 93 95
-33 90 81 105 96
-34 92 82 97 98
-35 99 80 93 95
-36 66 77 91 84
-37 83 74 87 98
-38 70 81 61 75
-39 104 94 95 86
-40 101 93 72 85
-41 104 97 108 87
-42 104 94 95 86
-43 77 100 92 71
-44 88 89 102 103
-45 90 81 105 96
-46 100 91 105 106
-47 88 89 102 103
-48 92 82 97 98
-49 90 70 83 65
-50 79 103 94 108
-51 101 106 96 107
-52 100 91 105 106
-53 104 97 108 87
-54 101 106 96 107
-55 1 12 2 20
-56 1 3 19 20
-57 1 4 7 20
-58 12 2 5 28
-59 11 1 6 20
-60 12 2 4 7
-61 3 38 8 19
-62 4 26 7 9
-63 12 2 18 10
-64 11 3 6 19
-65 13 5 49 28
-66 11 14 36 6
-67 4 15 17 7
-68 3 16 27 19
-69 5 28 18 10
-70 13 38 49 8
-71 26 9 21 43
-72 22 18 40 10
-73 11 23 25 6
-74 24 37 5 28
-75 16 27 38 8
-76 15 26 17 9
-77 14 36 21 43
-78 15 17 29 31
-79 16 27 50 30
-80 35 18 10 32
-81 33 45 38 8
-82 34 26 48 9
-83 13 24 37 49
-84 23 14 25 36
-85 22 29 40 31
-86 23 25 39 42
-87 24 37 41 53
-88 44 47 16 27
-89 44 47 15 17
-90 33 45 13 49
-91 46 14 36 52
-92 34 48 21 43
-93 22 35 40 32
-94 39 50 30 42
-95 35 39 42 32
-96 33 45 51 54
-97 34 48 41 53
-98 34 24 37 48
-99 23 35 25 32
-100 46 52 21 43
-101 22 40 51 54
-102 44 47 29 31
-103 44 47 50 30
-104 39 41 42 53
-105 33 45 46 52
-106 46 51 52 54
-107 29 51 31 54
-108 50 30 41 53
0

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