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On this page are computer-accessible forms for the graph C4[ 64, 7 ] = MPS(4,32;7).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {32, 36} under the group generated by the following permutations:

a: (4, 40)(12, 48)(19, 63)(27, 55)
b: (4, 12)(19, 63)(20, 56)(27, 55)(28, 64)(40, 48)
c: (1, 2)(3, 8)(4, 7)(5, 6)(9, 10)(11, 16)(12, 15)(13, 14)(18, 52)(19, 23)(20, 22)(24, 54)(26, 60)(27, 31)(28, 30)(32, 62)(33, 42)(34, 41)(35, 40)(36, 39)(37, 46)(38, 45)(43, 48)(44, 47)(49, 57)(50, 56)(51, 55)(53, 61)(58, 64)(59, 63)
d: (3, 11)(18, 62)(19, 55)(26, 54)(27, 63)(39, 47)
e: (5, 33)(13, 41)(21, 57)(29, 49)
f: (5, 13)(20, 64)(21, 57)(28, 56)(29, 49)(33, 41)
g: (7, 35)(15, 43)(23, 59)(31, 51)
h: (6, 34)(14, 42)(22, 58)(30, 50)
m: (1, 17, 2, 18, 3, 19, 4, 20, 5, 21, 6, 22, 7, 23, 8, 24, 9, 25, 10, 26, 11, 27, 12, 28, 13, 29, 14, 30, 15, 31, 16, 32)(33, 49, 34, 50, 35, 51, 36, 52, 37, 53, 38, 54, 39, 55, 40, 56, 41, 57, 42, 58, 43, 59, 44, 60, 45, 61, 46, 62, 47, 63, 48, 64)
n1: (8, 36)(16, 44)(24, 60)(32, 52)
a1: (6, 14)(21, 49)(22, 58)(29, 57)(30, 50)(34, 42)
b1: (2, 8)(3, 7)(4, 6)(10, 16)(11, 15)(12, 14)(17, 52)(18, 23)(19, 22)(20, 21)(24, 53)(25, 60)(26, 31)(27, 30)(28, 29)(32, 61)(33, 41)(34, 40)(35, 39)(36, 38)(37, 45)(42, 48)(43, 47)(44, 46)(49, 56)(50, 55)(51, 54)(57, 64)(58, 63)(59, 62)
c1: (7, 15)(22, 50)(23, 59)(30, 58)(31, 51)(35, 43)
d1: (8, 16)(23, 51)(24, 60)(31, 59)(32, 52)(36, 44)
e1: (3, 39)(11, 47)(18, 62)(26, 54)

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

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