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On this page are computer-accessible forms for the graph C4[ 100, 7 ] = MSZ(20,5,9,2).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {2, 3} under the group generated by the following permutations:

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

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

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