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On this page are computer-accessible forms for the graph C4[ 112, 10 ] = SDD(W(14,2)).

(I) Following is a form readable by MAGMA:

g:=Graph<112|{ {46, 60}, {38, 62}, {32, 57}, {38, 58}, {32, 61}, {38, 59}, {38, 57}, {16, 58}, {19, 63}, {22, 59}, {19, 60}, {9, 61}, {11, 63}, {10, 62}, {10, 63}, {11, 62}, {1, 57}, {1, 59}, {7, 61}, {6, 60}, {1, 58}, {2, 57}, {3, 63}, {4, 58}, {5, 59}, {1, 62}, {3, 60}, {2, 61}, {4, 68}, {22, 86}, {18, 82}, {8, 72}, {6, 70}, {5, 69}, {33, 97}, {35, 99}, {36, 100}, {23, 86}, {44, 109}, {25, 88}, {2, 64}, {17, 83}, {7, 69}, {3, 65}, {34, 96}, {35, 97}, {21, 86}, {51, 112}, {44, 111}, {24, 91}, {27, 88}, {8, 76}, {35, 103}, {2, 71}, {43, 110}, {25, 92}, {12, 73}, {9, 76}, {8, 77}, {7, 66}, {26, 95}, {12, 74}, {44, 106}, {3, 68}, {55, 112}, {47, 104}, {45, 106}, {43, 108}, {20, 83}, {27, 92}, {29, 90}, {36, 99}, {39, 96}, {18, 90}, {20, 93}, {35, 106}, {4, 78}, {45, 103}, {29, 87}, {7, 76}, {9, 66}, {8, 67}, {30, 85}, {34, 105}, {9, 69}, {45, 97}, {44, 96}, {21, 89}, {18, 94}, {17, 93}, {15, 67}, {14, 66}, {13, 65}, {12, 64}, {4, 73}, {47, 98}, {6, 75}, {29, 80}, {31, 82}, {36, 105}, {23, 89}, {45, 99}, {43, 101}, {26, 84}, {39, 105}, {40, 102}, {5, 74}, {18, 93}, {30, 81}, {36, 107}, {11, 91}, {53, 101}, {23, 71}, {27, 75}, {6, 87}, {24, 73}, {10, 91}, {19, 65}, {56, 106}, {54, 100}, {25, 75}, {24, 74}, {21, 71}, {20, 70}, {5, 86}, {53, 102}, {48, 99}, {22, 69}, {28, 79}, {16, 68}, {48, 100}, {13, 88}, {56, 109}, {49, 100}, {27, 78}, {10, 92}, {11, 92}, {56, 111}, {53, 98}, {50, 101}, {25, 78}, {19, 68}, {17, 70}, {14, 89}, {12, 91}, {26, 77}, {24, 64}, {56, 96}, {55, 111}, {51, 107}, {16, 73}, {55, 110}, {49, 104}, {48, 105}, {14, 84}, {54, 108}, {15, 85}, {20, 79}, {54, 109}, {48, 107}, {22, 74}, {55, 107}, {51, 111}, {50, 110}, {49, 109}, {13, 80}, {51, 110}, {49, 108}, {21, 72}, {30, 67}, {13, 83}, {54, 104}, {50, 108}, {17, 79}, {16, 78}, {15, 81}, {14, 81}, {47, 112}, {23, 72}, {32, 64}, {46, 75}, {37, 67}, {52, 82}, {32, 71}, {15, 103}, {46, 70}, {37, 77}, {41, 65}, {42, 66}, {37, 76}, {52, 93}, {52, 94}, {33, 77}, {50, 94}, {37, 72}, {52, 90}, {31, 112}, {41, 88}, {39, 85}, {40, 90}, {42, 89}, {33, 84}, {43, 94}, {31, 104}, {34, 85}, {39, 95}, {40, 80}, {28, 101}, {46, 87}, {30, 103}, {41, 80}, {28, 102}, {53, 79}, {41, 83}, {26, 97}, {29, 102}, {42, 81}, {31, 98}, {47, 82}, {34, 95}, {28, 98}, {42, 84}, {33, 95}, {40, 87} }>;

(II) A more general form is to represent the graph as the orbit of {46, 60} under the group generated by the following permutations:

a: (26, 33)
b: (14, 42)
c: (35, 45)
d: (12, 24)
e: (28, 53)
f: (4, 10)(11, 16)(58, 62)(63, 68)(73, 91)(78, 92)
g: (18, 28)(52, 53)(79, 93)(82, 98)(90, 102)(94, 101)
h: (25, 27)
m: (7, 9)
n1: (51, 55)
a1: (21, 23)
b1: (3, 19)
c1: (49, 51)(54, 55)(100, 107)(104, 112)(108, 110)(109, 111)
d1: (7, 21)(9, 23)(61, 71)(66, 89)(69, 86)(72, 76)
e1: (13, 41)
f1: (8, 14)(37, 42)(66, 76)(67, 81)(72, 89)(77, 84)
g1: (43, 50)
h1: (6, 13)(41, 46)(60, 65)(70, 83)(75, 88)(80, 87)
m1: (17, 20)
n2: (15, 26)(30, 33)(67, 77)(81, 84)(85, 95)(97, 103)
a2: (34, 35)(39, 45)(85, 103)(95, 97)(96, 106)(99, 105)
b2: (3, 25)(19, 27)(60, 75)(63, 92)(65, 88)(68, 78)
c2: (5, 22)
d2: (17, 29)(20, 40)(70, 87)(79, 102)(80, 83)(90, 93)
e2: (29, 40)
f2: (44, 56)
g2: (1, 2)(3, 8)(4, 7)(5, 12)(6, 15)(9, 16)(10, 21)(11, 23)(13, 26)(14, 25)(17, 34)(18, 36)(19, 37)(20, 39)(22, 24)(27, 42)(28, 44)(29, 35)(30, 46)(31, 49)(32, 38)(33, 41)(40, 45)(43, 51)(47, 54)(48, 52)(50, 55)(53, 56)(58, 61)(59, 64)(60, 67)(62, 71)(63, 72)(65, 77)(66, 78)(68, 76)(69, 73)(70, 85)(75, 81)(79, 96)(80, 97)(82, 100)(83, 95)(84, 88)(86, 91)(87, 103)(89, 92)(90, 99)(93, 105)(94, 107)(98, 109)(101, 111)(102, 106)(108, 112)
h2: (36, 44)(48, 56)(96, 105)(99, 106)(100, 109)(107, 111)
m2: (31, 43)(47, 50)(82, 94)(98, 101)(104, 108)(110, 112)
n3: (10, 11)
a3: (2, 4)(3, 7)(5, 10)(6, 8)(9, 19)(11, 22)(13, 14)(15, 17)(16, 32)(18, 34)(20, 30)(21, 25)(23, 27)(26, 29)(28, 35)(31, 36)(33, 40)(37, 46)(39, 52)(41, 42)(43, 44)(45, 53)(47, 48)(50, 56)(57, 58)(59, 62)(60, 76)(61, 68)(63, 69)(64, 73)(65, 66)(67, 70)(71, 78)(72, 75)(74, 91)(77, 87)(79, 103)(80, 84)(81, 83)(82, 105)(85, 93)(86, 92)(88, 89)(90, 95)(94, 96)(97, 102)(98, 99)(100, 104)(101, 106)(107, 112)(108, 109)(110, 111)

(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.

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&Graph
C4[ 112, 10 ]
112
-1 57 58 59 62
-2 57 71 61 64
-3 68 60 63 65
-4 78 68 58 73
-5 69 59 74 86
-6 70 60 75 87
-7 66 69 61 76
-8 77 67 72 76
-9 66 69 61 76
-10 91 92 62 63
-11 91 92 62 63
-12 91 73 74 64
-13 88 80 83 65
-14 66 89 81 84
-15 67 81 103 85
-16 78 68 58 73
-17 79 70 93 83
-18 90 82 93 94
-19 68 60 63 65
-20 79 70 93 83
-21 89 71 72 86
-22 69 59 74 86
-23 89 71 72 86
-24 91 73 74 64
-25 88 78 92 75
-26 77 84 95 97
-27 88 78 92 75
-28 79 101 102 98
-29 90 80 102 87
-30 67 81 103 85
-31 112 82 104 98
-32 57 71 61 64
-33 77 84 95 97
-34 105 95 85 96
-35 99 103 106 97
-36 99 100 105 107
-37 77 67 72 76
-38 57 58 59 62
-39 105 95 85 96
-40 90 80 102 87
-41 88 80 83 65
-42 66 89 81 84
-43 110 101 94 108
-44 111 106 96 109
-45 99 103 106 97
-46 70 60 75 87
-47 112 82 104 98
-48 99 100 105 107
-49 100 104 108 109
-50 110 101 94 108
-51 110 111 112 107
-52 90 82 93 94
-53 79 101 102 98
-54 100 104 108 109
-55 110 111 112 107
-56 111 106 96 109
-57 1 2 38 32
-58 1 4 16 38
-59 22 1 5 38
-60 46 3 6 19
-61 2 7 9 32
-62 11 1 38 10
-63 11 3 19 10
-64 12 2 24 32
-65 13 3 19 41
-66 14 7 9 42
-67 15 37 8 30
-68 3 4 16 19
-69 22 5 7 9
-70 46 6 17 20
-71 23 2 21 32
-72 23 37 8 21
-73 12 24 4 16
-74 22 12 24 5
-75 46 25 27 6
-76 37 7 8 9
-77 33 26 37 8
-78 25 4 16 27
-79 17 28 20 53
-80 13 29 40 41
-81 14 15 30 42
-82 47 18 52 31
-83 13 17 41 20
-84 33 14 26 42
-85 34 15 39 30
-86 22 23 5 21
-87 46 6 29 40
-88 13 25 27 41
-89 23 14 42 21
-90 18 29 40 52
-91 11 12 24 10
-92 11 25 27 10
-93 17 18 52 20
-94 50 18 52 43
-95 33 34 26 39
-96 44 34 56 39
-97 33 45 35 26
-98 47 28 31 53
-99 45 35 36 48
-100 36 48 49 54
-101 28 50 53 43
-102 28 29 40 53
-103 45 35 15 30
-104 47 49 31 54
-105 34 36 48 39
-106 44 45 56 35
-107 55 36 48 51
-108 49 50 43 54
-109 44 56 49 54
-110 55 50 51 43
-111 44 55 56 51
-112 55 47 51 31
0

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