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On this page are computer-accessible forms for the graph C4[ 72, 20 ] = UG(ATD[72,1]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {6, 7} under the group generated by the following permutations:

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

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

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