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On this page are computer-accessible forms for the graph C4[ 108, 8 ] = R_54(29,28).

(I) Following is a form readable by MAGMA:

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

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

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

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