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On this page are computer-accessible forms for the graph C4[ 72, 18 ] = AMC(8,3,[0.1:1.2]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {36, 37} under the group generated by the following permutations:

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

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

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