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On this page are computer-accessible forms for the graph C4[ 56, 5 ] = PX(7,3).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {8, 15} under the group generated by the following permutations:

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

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

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