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On this page are computer-accessible forms for the graph C4[ 72, 19 ] = AMC(4,12,[1.8:4.1]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {36, 38} under the group generated by the following permutations:

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

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

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

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