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On this page are computer-accessible forms for the graph C4[ 72, 4 ] = DW(24,3).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {24, 25} under the group generated by the following permutations:

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

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

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