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On this page are computer-accessible forms for the graph C4[ 56, 4 ] = R_28(16,15).

(I) Following is a form readable by MAGMA:

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

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

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

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