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On this page are computer-accessible forms for the graph C4[ 72, 13 ] = Pr_24(1,1,5,5).

(I) Following is a form readable by MAGMA:

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

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

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

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