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On this page are computer-accessible forms for the graph C4[ 72, 21 ] = UG(ATD[72,13]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {10, 11} under the group generated by the following permutations:

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

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

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