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On this page are computer-accessible forms for the graph C4[ 72, 8 ] = PS(6,24;7).

(I) Following is a form readable by MAGMA:

g:=Graph<72|{ {24, 28}, {48, 52}, {16, 25}, {22, 31}, {20, 29}, {18, 27}, {48, 57}, {4, 15}, {32, 43}, {21, 30}, {17, 26}, {36, 47}, {52, 63}, {1, 13}, {34, 46}, {33, 45}, {32, 44}, {23, 27}, {22, 26}, {21, 25}, {2, 14}, {3, 15}, {35, 47}, {49, 61}, {50, 62}, {51, 63}, {3, 14}, {33, 44}, {35, 46}, {51, 62}, {2, 13}, {34, 45}, {19, 28}, {50, 61}, {13, 29}, {14, 30}, {15, 31}, {37, 53}, {38, 54}, {39, 55}, {40, 56}, {41, 57}, {42, 58}, {43, 59}, {44, 60}, {4, 16}, {5, 17}, {6, 18}, {7, 19}, {12, 24}, {36, 48}, {5, 16}, {7, 18}, {6, 17}, {47, 56}, {1, 24}, {40, 49}, {42, 51}, {44, 53}, {46, 55}, {8, 19}, {12, 23}, {39, 60}, {41, 50}, {45, 54}, {8, 20}, {9, 21}, {10, 22}, {11, 23}, {45, 49}, {46, 50}, {47, 51}, {9, 20}, {11, 22}, {38, 59}, {10, 21}, {37, 58}, {43, 52}, {25, 48}, {15, 36}, {14, 35}, {13, 34}, {16, 32}, {20, 36}, {19, 35}, {17, 33}, {18, 34}, {12, 63}, {28, 40}, {31, 43}, {30, 42}, {29, 41}, {11, 62}, {31, 42}, {29, 40}, {10, 61}, {30, 41}, {23, 32}, {5, 61}, {6, 62}, {7, 63}, {24, 33}, {28, 39}, {25, 37}, {27, 39}, {26, 38}, {27, 38}, {26, 37}, {1, 64}, {3, 66}, {5, 68}, {7, 70}, {9, 72}, {2, 65}, {6, 69}, {1, 69}, {2, 70}, {3, 71}, {4, 67}, {8, 64}, {9, 65}, {10, 66}, {11, 67}, {12, 68}, {4, 72}, {8, 71}, {52, 64}, {60, 72}, {53, 65}, {54, 66}, {55, 67}, {53, 64}, {55, 66}, {54, 65}, {49, 72}, {56, 67}, {60, 71}, {56, 68}, {57, 69}, {58, 70}, {59, 71}, {57, 68}, {59, 70}, {58, 69} }>;

(II) A more general form is to represent the graph as the orbit of {24, 28} under the group generated by the following permutations:

a: (2, 12)(3, 11)(4, 10)(5, 9)(6, 8)(13, 24)(14, 23)(15, 22)(16, 21)(17, 20)(18, 19)(26, 36)(27, 35)(28, 34)(29, 33)(30, 32)(37, 48)(38, 47)(39, 46)(40, 45)(41, 44)(42, 43)(50, 60)(51, 59)(52, 58)(53, 57)(54, 56)(61, 72)(62, 71)(63, 70)(64, 69)(65, 68)(66, 67)
b: (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, 57, 58, 59, 60)(61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72)
c: (2, 28, 6, 52)(3, 55, 11, 31)(4, 10)(5, 25, 9, 49)(8, 34, 12, 58)(13, 24, 69, 64)(14, 39, 62, 43)(15, 66, 67, 22)(16, 21, 72, 61)(17, 48, 65, 40)(18, 63, 70, 19)(20, 45, 68, 37)(23, 42, 71, 46)(26, 36, 54, 56)(27, 51, 59, 35)(29, 33, 57, 53)(30, 60, 50, 32)(38, 47)(41, 44)
d: (1, 13, 2, 14, 3, 15, 4, 16, 5, 17, 6, 18, 7, 19, 8, 20, 9, 21, 10, 22, 11, 23, 12, 24)(25, 61, 26, 62, 27, 63, 28, 64, 29, 65, 30, 66, 31, 67, 32, 68, 33, 69, 34, 70, 35, 71, 36, 72)(37, 50, 38, 51, 39, 52, 40, 53, 41, 54, 42, 55, 43, 56, 44, 57, 45, 58, 46, 59, 47, 60, 48, 49)

(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[ 72, 8 ]
72
-1 13 24 69 64
-2 13 14 70 65
-3 66 14 15 71
-4 67 15 16 72
-5 68 16 17 61
-6 69 17 18 62
-7 70 18 19 63
-8 71 19 20 64
-9 72 20 21 65
-10 22 66 61 21
-11 22 23 67 62
-12 23 24 68 63
-13 1 34 2 29
-14 2 35 3 30
-15 3 36 4 31
-16 25 4 5 32
-17 33 26 5 6
-18 34 27 6 7
-19 35 28 7 8
-20 36 29 8 9
-21 25 30 9 10
-22 11 26 31 10
-23 11 12 27 32
-24 33 1 12 28
-25 37 48 16 21
-26 22 37 38 17
-27 23 38 39 18
-28 24 39 40 19
-29 13 40 41 20
-30 14 41 42 21
-31 22 15 42 43
-32 44 23 16 43
-33 44 45 24 17
-34 45 13 46 18
-35 46 14 47 19
-36 47 15 48 20
-37 25 58 26 53
-38 26 59 27 54
-39 55 27 60 28
-40 56 49 28 29
-41 57 50 29 30
-42 58 51 30 31
-43 59 52 31 32
-44 33 60 53 32
-45 33 34 49 54
-46 55 34 35 50
-47 56 35 36 51
-48 57 25 36 52
-49 45 61 72 40
-50 46 61 62 41
-51 47 62 63 42
-52 48 63 64 43
-53 44 37 64 65
-54 66 45 38 65
-55 66 67 46 39
-56 67 68 47 40
-57 68 69 48 41
-58 69 37 70 42
-59 70 38 71 43
-60 44 71 39 72
-61 5 49 50 10
-62 11 6 50 51
-63 12 7 51 52
-64 1 8 52 53
-65 2 9 53 54
-66 55 3 10 54
-67 11 55 56 4
-68 12 56 57 5
-69 1 57 58 6
-70 2 58 59 7
-71 3 59 60 8
-72 4 49 60 9
0

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