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On this page are computer-accessible forms for the graph C4[ 72, 26 ] = BGCG(AMC(4,3,[0.1:1.2]);K1;1).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {35, 39} under the group generated by the following permutations:

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

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

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