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On this page are computer-accessible forms for the graph C4[ 72, 22 ] = PL(ATD[6,1]#DCyc[3]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {33, 37} under the group generated by the following permutations:

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

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

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