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On this page are computer-accessible forms for the graph C4[ 104, 12 ] = SDD(C_26(1,5)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {28, 63} under the group generated by the following permutations:

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

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

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