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On this page are computer-accessible forms for the graph C4[ 116, 4 ] = SDD(C_29(1,12)).

(I) Following is a form readable by MAGMA:

g:=Graph<116|{ {16, 63}, {15, 63}, {14, 63}, {12, 62}, {13, 62}, {9, 61}, {11, 63}, {8, 61}, {11, 62}, {8, 62}, {10, 61}, {3, 59}, {5, 61}, {2, 59}, {5, 60}, {1, 59}, {6, 60}, {7, 60}, {1, 60}, {4, 59}, {9, 73}, {16, 80}, {34, 98}, {35, 99}, {13, 79}, {19, 81}, {32, 98}, {38, 100}, {32, 99}, {33, 98}, {38, 101}, {39, 100}, {10, 78}, {44, 104}, {22, 82}, {15, 75}, {2, 71}, {12, 74}, {55, 113}, {54, 112}, {46, 104}, {25, 95}, {37, 99}, {24, 95}, {55, 112}, {47, 104}, {46, 105}, {35, 100}, {36, 99}, {22, 94}, {28, 84}, {23, 95}, {56, 113}, {58, 115}, {7, 77}, {57, 115}, {56, 114}, {45, 103}, {25, 83}, {20, 94}, {31, 85}, {20, 95}, {57, 114}, {44, 103}, {21, 94}, {36, 111}, {16, 92}, {17, 93}, {41, 101}, {42, 102}, {40, 101}, {43, 102}, {42, 103}, {6, 72}, {58, 116}, {19, 93}, {14, 64}, {30, 80}, {40, 102}, {3, 76}, {18, 93}, {17, 94}, {33, 110}, {10, 90}, {17, 65}, {11, 91}, {17, 64}, {34, 115}, {37, 116}, {8, 90}, {18, 64}, {14, 92}, {4, 87}, {19, 64}, {15, 92}, {14, 93}, {9, 90}, {8, 91}, {21, 65}, {27, 79}, {23, 67}, {20, 65}, {23, 66}, {13, 91}, {24, 78}, {20, 66}, {11, 92}, {22, 65}, {12, 91}, {39, 112}, {1, 89}, {29, 69}, {27, 67}, {21, 77}, {41, 113}, {1, 88}, {54, 111}, {52, 109}, {50, 107}, {48, 105}, {43, 114}, {29, 68}, {26, 67}, {2, 88}, {53, 111}, {52, 110}, {49, 107}, {48, 106}, {24, 66}, {30, 68}, {3, 88}, {53, 110}, {49, 106}, {47, 116}, {25, 66}, {31, 68}, {4, 88}, {5, 89}, {7, 89}, {51, 109}, {50, 108}, {45, 115}, {26, 68}, {18, 76}, {5, 90}, {51, 108}, {28, 67}, {6, 89}, {39, 71}, {40, 72}, {42, 74}, {10, 107}, {13, 108}, {38, 71}, {40, 73}, {41, 72}, {36, 70}, {46, 76}, {43, 73}, {6, 101}, {55, 84}, {51, 80}, {37, 70}, {42, 73}, {33, 69}, {55, 83}, {54, 82}, {53, 81}, {52, 80}, {47, 75}, {35, 71}, {32, 69}, {54, 83}, {52, 81}, {46, 75}, {35, 70}, {2, 100}, {44, 74}, {32, 70}, {15, 104}, {53, 82}, {45, 74}, {44, 75}, {34, 69}, {25, 112}, {3, 105}, {12, 103}, {56, 84}, {58, 86}, {57, 85}, {7, 106}, {58, 87}, {56, 85}, {28, 113}, {31, 114}, {38, 72}, {9, 102}, {57, 86}, {4, 116}, {33, 81}, {37, 87}, {24, 107}, {30, 109}, {34, 86}, {39, 83}, {36, 82}, {23, 96}, {27, 108}, {47, 87}, {22, 111}, {26, 96}, {18, 105}, {45, 86}, {27, 96}, {26, 97}, {28, 96}, {51, 79}, {50, 78}, {49, 77}, {48, 76}, {29, 97}, {16, 109}, {50, 79}, {48, 77}, {19, 110}, {41, 84}, {31, 97}, {43, 85}, {21, 106}, {49, 78}, {29, 98}, {30, 97} }>;

(II) A more general form is to represent the graph as the orbit of {16, 63} under the group generated by the following permutations:

a: (83, 112)
b: (70, 99)
c: (60, 89)
d: (80, 109)
e: (81, 110)
f: (59, 88)
g: (73, 102)
h: (87, 116)
m: (74, 103)
n1: (66, 95)
a1: (63, 92)
b1: (71, 100)
c1: (84, 113)
d1: (67, 96)
e1: (78, 107)
f1: (72, 101)
g1: (2, 7)(3, 6)(4, 5)(8, 58)(9, 47)(10, 37)(11, 57)(12, 45)(13, 34)(14, 56)(15, 43)(16, 31)(17, 55)(18, 41)(19, 28)(20, 54)(21, 39)(22, 25)(23, 53)(24, 36)(26, 52)(27, 33)(29, 51)(32, 50)(35, 49)(38, 48)(40, 46)(42, 44)(59, 60)(61, 87)(62, 86)(63, 85)(64, 84)(65, 83)(66, 82)(67, 81)(68, 80)(69, 79)(70, 78)(71, 77)(72, 76)(73, 75)(88, 89)(90, 116)(91, 115)(92, 114)(93, 113)(94, 112)(95, 111)(96, 110)(97, 109)(98, 108)(99, 107)(100, 106)(101, 105)(102, 104)
h1: (61, 90)
m1: (64, 93)
n2: (82, 111)
a2: (1, 2, 4, 3)(5, 39, 58, 18)(6, 35, 47, 48)(7, 38, 37, 46)(8, 25, 57, 19)(9, 54, 45, 17)(10, 55, 34, 14)(11, 24, 56, 33)(12, 20, 43, 53)(13, 23, 31, 52)(15, 49, 41, 32)(16, 50, 28, 29)(21, 40, 36, 44)(22, 42)(26, 30, 51, 27)(60, 71, 87, 76)(61, 83, 86, 64)(62, 66, 85, 81)(63, 78, 84, 69)(65, 73, 82, 74)(67, 68, 80, 79)(70, 75, 77, 72)(89, 100, 116, 105)(90, 112, 115, 93)(91, 95, 114, 110)(92, 107, 113, 98)(94, 102, 111, 103)(96, 97, 109, 108)(99, 104, 106, 101)
b2: (85, 114)
c2: (65, 94)
d2: (79, 108)
e2: (86, 115)
f2: (76, 105)
g2: (75, 104)
h2: (62, 91)
m2: (68, 97)
n3: (77, 106)

(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[ 116, 4 ]
116
-1 88 89 59 60
-2 88 100 59 71
-3 88 59 105 76
-4 88 59 116 87
-5 89 90 60 61
-6 89 101 60 72
-7 77 89 60 106
-8 90 91 61 62
-9 90 102 61 73
-10 78 90 61 107
-11 91 92 62 63
-12 91 103 62 74
-13 79 91 62 108
-14 92 93 63 64
-15 92 104 63 75
-16 80 92 63 109
-17 93 94 64 65
-18 93 105 64 76
-19 110 81 93 64
-20 66 94 95 65
-21 77 94 106 65
-22 111 82 94 65
-23 66 67 95 96
-24 66 78 95 107
-25 66 112 83 95
-26 67 68 96 97
-27 67 79 96 108
-28 67 113 84 96
-29 68 69 97 98
-30 68 80 97 109
-31 68 114 85 97
-32 99 69 70 98
-33 110 69 81 98
-34 69 115 86 98
-35 99 100 70 71
-36 99 111 70 82
-37 99 70 116 87
-38 100 101 71 72
-39 100 112 71 83
-40 101 102 72 73
-41 101 113 72 84
-42 102 103 73 74
-43 102 114 73 85
-44 103 104 74 75
-45 103 115 74 86
-46 104 105 75 76
-47 104 116 75 87
-48 77 105 106 76
-49 77 78 106 107
-50 78 79 107 108
-51 79 80 108 109
-52 110 80 81 109
-53 110 111 81 82
-54 111 112 82 83
-55 112 113 83 84
-56 113 114 84 85
-57 114 115 85 86
-58 115 116 86 87
-59 1 2 3 4
-60 1 5 6 7
-61 5 8 9 10
-62 11 12 13 8
-63 11 14 15 16
-64 14 17 18 19
-65 22 17 20 21
-66 23 24 25 20
-67 23 26 27 28
-68 26 29 30 31
-69 33 34 29 32
-70 35 36 37 32
-71 2 35 38 39
-72 38 6 40 41
-73 40 9 42 43
-74 44 12 45 42
-75 44 46 47 15
-76 46 3 48 18
-77 48 49 7 21
-78 24 49 50 10
-79 13 27 50 51
-80 16 51 30 52
-81 33 19 52 53
-82 22 36 53 54
-83 55 25 39 54
-84 55 56 28 41
-85 56 57 31 43
-86 34 45 57 58
-87 47 58 4 37
-88 1 2 3 4
-89 1 5 6 7
-90 5 8 9 10
-91 11 12 13 8
-92 11 14 15 16
-93 14 17 18 19
-94 22 17 20 21
-95 23 24 25 20
-96 23 26 27 28
-97 26 29 30 31
-98 33 34 29 32
-99 35 36 37 32
-100 2 35 38 39
-101 38 6 40 41
-102 40 9 42 43
-103 44 12 45 42
-104 44 46 47 15
-105 46 3 48 18
-106 48 49 7 21
-107 24 49 50 10
-108 13 27 50 51
-109 16 51 30 52
-110 33 19 52 53
-111 22 36 53 54
-112 55 25 39 54
-113 55 56 28 41
-114 56 57 31 43
-115 34 45 57 58
-116 47 58 4 37
0

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