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On this page are computer-accessible forms for the graph C4[ 55, 4 ] = MSY(5,11,5,0).

(I) Following is a form readable by MAGMA:

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

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

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

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