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On this page are computer-accessible forms for the graph C4[ 100, 6 ] = R_50(27,26).

(I) Following is a form readable by MAGMA:

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

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

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

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