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On this page are computer-accessible forms for the graph C4[ 75, 3 ] = AMC(3,5,[0.1:4.4]).

(I) Following is a form readable by MAGMA:

g:=Graph<75|{ {24, 29}, {25, 30}, {23, 28}, {22, 27}, {21, 26}, {8, 28}, {9, 29}, {10, 30}, {11, 31}, {40, 61}, {32, 56}, {33, 57}, {34, 58}, {35, 59}, {37, 61}, {38, 62}, {39, 63}, {32, 58}, {33, 59}, {36, 62}, {37, 63}, {35, 56}, {6, 26}, {7, 27}, {1, 31}, {34, 60}, {21, 52}, {23, 54}, {2, 32}, {19, 49}, {18, 48}, {15, 45}, {3, 33}, {6, 36}, {7, 37}, {10, 40}, {11, 41}, {14, 44}, {22, 53}, {31, 60}, {4, 34}, {20, 50}, {5, 35}, {12, 42}, {13, 43}, {31, 57}, {27, 51}, {28, 52}, {29, 53}, {30, 54}, {25, 51}, {28, 54}, {29, 55}, {12, 32}, {19, 63}, {18, 62}, {17, 61}, {15, 35}, {13, 33}, {14, 34}, {2, 47}, {26, 55}, {30, 51}, {8, 38}, {9, 39}, {26, 52}, {27, 53}, {1, 46}, {24, 55}, {6, 55}, {3, 48}, {7, 51}, {19, 39}, {18, 38}, {17, 37}, {16, 36}, {15, 59}, {14, 58}, {12, 56}, {13, 57}, {24, 44}, {25, 45}, {4, 49}, {5, 50}, {10, 61}, {11, 60}, {1, 57}, {2, 58}, {3, 59}, {4, 60}, {6, 62}, {7, 63}, {8, 52}, {22, 42}, {21, 41}, {20, 40}, {9, 53}, {10, 54}, {23, 43}, {5, 56}, {16, 46}, {17, 47}, {2, 71}, {8, 64}, {14, 70}, {9, 65}, {11, 67}, {12, 68}, {13, 69}, {1, 75}, {3, 72}, {4, 73}, {15, 66}, {5, 74}, {16, 65}, {20, 71}, {21, 70}, {20, 64}, {22, 66}, {23, 67}, {16, 72}, {19, 75}, {18, 74}, {17, 73}, {24, 68}, {25, 69}, {36, 65}, {46, 75}, {38, 64}, {39, 65}, {46, 72}, {47, 73}, {40, 64}, {42, 66}, {43, 67}, {44, 68}, {45, 69}, {47, 71}, {41, 67}, {44, 70}, {42, 68}, {43, 69}, {41, 70}, {45, 66}, {50, 71}, {48, 72}, {50, 74}, {49, 73}, {48, 74}, {49, 75} }>;

(II) A more general form is to represent the graph as the orbit of {24, 29} under the group generated by the following permutations:

a: (1, 6, 5, 10, 4, 9, 3, 8, 2, 7)(11, 24, 15, 23, 14, 22, 13, 21, 12, 25)(16, 18, 20, 17, 19)(26, 56, 30, 60, 29, 59, 28, 58, 27, 57)(31, 55, 35, 54, 34, 53, 33, 52, 32, 51)(36, 74, 40, 73, 39, 72, 38, 71, 37, 75)(41, 68, 45, 67, 44, 66, 43, 70, 42, 69)(46, 62, 50, 61, 49, 65, 48, 64, 47, 63)
b: (1, 26)(2, 32)(3, 38)(4, 44)(5, 50)(6, 46)(7, 27)(8, 33)(9, 39)(10, 45)(11, 41)(12, 47)(13, 28)(14, 34)(15, 40)(16, 36)(17, 42)(18, 48)(19, 29)(20, 35)(21, 31)(22, 37)(23, 43)(24, 49)(25, 30)(52, 57)(53, 63)(54, 69)(55, 75)(56, 71)(59, 64)(60, 70)(61, 66)(62, 72)(68, 73)
c: (6, 25)(7, 21)(8, 22)(9, 23)(10, 24)(11, 19)(12, 20)(13, 16)(14, 17)(15, 18)(26, 51)(27, 52)(28, 53)(29, 54)(30, 55)(31, 75)(32, 71)(33, 72)(34, 73)(35, 74)(36, 69)(37, 70)(38, 66)(39, 67)(40, 68)(41, 63)(42, 64)(43, 65)(44, 61)(45, 62)(46, 57)(47, 58)(48, 59)(49, 60)(50, 56)
d: (1, 2)(3, 5)(6, 8)(9, 10)(11, 14)(12, 13)(16, 20)(17, 19)(22, 25)(23, 24)(26, 52)(27, 51)(28, 55)(29, 54)(30, 53)(31, 58)(32, 57)(33, 56)(34, 60)(35, 59)(36, 64)(37, 63)(38, 62)(39, 61)(40, 65)(41, 70)(42, 69)(43, 68)(44, 67)(45, 66)(46, 71)(47, 75)(48, 74)(49, 73)(50, 72)
e: (2, 5)(3, 4)(6, 7)(8, 10)(11, 13)(14, 15)(16, 19)(17, 18)(21, 25)(22, 24)(26, 51)(27, 55)(28, 54)(29, 53)(30, 52)(31, 57)(32, 56)(33, 60)(34, 59)(35, 58)(36, 63)(37, 62)(38, 61)(39, 65)(40, 64)(41, 69)(42, 68)(43, 67)(44, 66)(45, 70)(46, 75)(47, 74)(48, 73)(49, 72)(50, 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.

**************

&Graph
C4[ 75, 3 ]
75
-1 46 57 31 75
-2 47 58 71 32
-3 33 48 59 72
-4 34 49 60 73
-5 56 35 50 74
-6 55 36 26 62
-7 37 27 51 63
-8 38 28 52 64
-9 39 29 53 65
-10 61 40 30 54
-11 67 60 41 31
-12 56 68 42 32
-13 33 57 69 43
-14 44 34 58 70
-15 66 45 35 59
-16 46 36 72 65
-17 47 37 61 73
-18 48 38 62 74
-19 49 39 63 75
-20 71 50 40 64
-21 26 70 41 52
-22 66 27 42 53
-23 67 28 43 54
-24 44 55 68 29
-25 45 69 51 30
-26 55 6 52 21
-27 22 7 51 53
-28 23 8 52 54
-29 55 24 9 53
-30 25 51 10 54
-31 11 1 57 60
-32 12 56 2 58
-33 13 57 3 59
-34 14 58 4 60
-35 56 15 59 5
-36 16 6 62 65
-37 17 61 7 63
-38 18 62 8 64
-39 19 63 9 65
-40 61 20 64 10
-41 11 67 70 21
-42 22 66 12 68
-43 23 67 13 69
-44 24 68 14 70
-45 66 25 69 15
-46 1 16 72 75
-47 2 71 17 73
-48 3 72 18 74
-49 4 73 19 75
-50 5 71 74 20
-51 25 27 7 30
-52 26 28 8 21
-53 22 27 29 9
-54 23 28 30 10
-55 24 26 6 29
-56 12 35 5 32
-57 33 1 13 31
-58 34 2 14 32
-59 33 35 3 15
-60 11 34 4 31
-61 37 17 40 10
-62 36 38 6 18
-63 37 39 7 19
-64 38 40 8 20
-65 36 16 39 9
-66 22 45 15 42
-67 11 23 41 43
-68 44 12 24 42
-69 45 13 25 43
-70 44 14 41 21
-71 2 47 50 20
-72 46 3 48 16
-73 47 4 49 17
-74 48 5 50 18
-75 1 46 49 19
0

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