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On this page are computer-accessible forms for the graph C4[ 64, 15 ] = UG(ATD[64,10]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {14, 15} under the group generated by the following permutations:

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

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

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