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On this page are computer-accessible forms for the graph C4[ 72, 27 ] = BGCG(AMC(4,3,[0.1:1.2]);K1;{2,3}).

(I) Following is a form readable by MAGMA:

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

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

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