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On this page are computer-accessible forms for the graph C4[ 104, 6 ] = MPS(4,52;5).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {52, 55} under the group generated by the following permutations:

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

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

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