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On this page are computer-accessible forms for the graph C4[ 72, 7 ] = PS(6,24;5).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {24, 27} under the group generated by the following permutations:

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

**************

&Graph
C4[ 72, 7 ]
72
-1 13 24 70 63
-2 13 14 71 64
-3 14 15 72 65
-4 66 15 16 61
-5 67 16 17 62
-6 68 17 18 63
-7 69 18 19 64
-8 70 19 20 65
-9 66 71 20 21
-10 22 67 72 21
-11 22 23 68 61
-12 23 24 69 62
-13 1 2 35 28
-14 2 3 36 29
-15 3 25 4 30
-16 4 26 5 31
-17 5 27 6 32
-18 33 6 28 7
-19 34 7 29 8
-20 35 8 30 9
-21 36 9 31 10
-22 11 25 10 32
-23 11 33 12 26
-24 1 12 34 27
-25 22 15 37 48
-26 23 37 16 38
-27 24 38 17 39
-28 13 39 18 40
-29 14 40 19 41
-30 15 41 20 42
-31 16 42 21 43
-32 22 44 17 43
-33 44 23 45 18
-34 45 24 46 19
-35 13 46 47 20
-36 14 47 48 21
-37 25 26 59 52
-38 26 27 60 53
-39 27 49 28 54
-40 55 28 50 29
-41 56 29 51 30
-42 57 30 52 31
-43 58 31 53 32
-44 33 59 32 54
-45 33 55 34 60
-46 34 56 35 49
-47 35 57 36 50
-48 25 36 58 51
-49 46 39 61 72
-50 47 61 40 62
-51 48 62 41 63
-52 37 63 42 64
-53 38 64 43 65
-54 44 66 39 65
-55 66 45 67 40
-56 67 46 68 41
-57 68 47 69 42
-58 69 48 70 43
-59 44 37 70 71
-60 45 38 71 72
-61 11 4 49 50
-62 12 5 50 51
-63 1 6 51 52
-64 2 7 52 53
-65 3 8 53 54
-66 55 4 9 54
-67 55 56 5 10
-68 11 56 57 6
-69 12 57 58 7
-70 1 58 59 8
-71 2 59 60 9
-72 3 49 60 10
0

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