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On this page are computer-accessible forms for the graph C4[ 112, 6 ] = MPS(4,56;13).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {56, 63} under the group generated by the following permutations:

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

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

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