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On this page are computer-accessible forms for the graph C4[ 72, 23 ] = SDD(DW(6,3)).

(I) Following is a form readable by MAGMA:

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

(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: (3, 31)
b: (18, 26)
c: (13, 28)
d: (12, 17)
e: (16, 19)
f: (1, 2)(3, 5)(4, 7)(6, 10)(8, 12)(9, 14)(11, 16)(13, 18)(15, 21)(17, 22)(19, 24)(20, 25)(23, 29)(26, 28)(27, 31)(30, 33)(32, 35)(34, 36)(38, 40)(39, 42)(41, 45)(43, 48)(44, 50)(46, 53)(47, 55)(49, 58)(51, 61)(52, 54)(57, 63)(60, 64)(62, 67)(65, 68)(69, 70)(71, 72)
g: (2, 34)
h: (8, 22)
m: (7, 30)
n1: (10, 32)
a1: (9, 25)
b1: (11, 24)
c1: (4, 33)
d1: (21, 23)
e1: (2, 3)(4, 6)(5, 8)(7, 11)(9, 13)(10, 15)(14, 16)(18, 21)(19, 20)(22, 27)(23, 26)(24, 30)(25, 28)(29, 32)(31, 34)(33, 35)(37, 38)(39, 41)(40, 43)(42, 46)(44, 49)(45, 51)(47, 54)(48, 56)(50, 59)(52, 62)(53, 63)(55, 60)(57, 65)(58, 66)(61, 68)(64, 70)(67, 71)(69, 72)
f1: (4, 6)(7, 10)(9, 13)(11, 15)(14, 18)(16, 21)(19, 23)(20, 26)(24, 29)(25, 28)(30, 32)(33, 35)(39, 41)(42, 45)(44, 49)(46, 51)(47, 62)(50, 58)(52, 54)(53, 61)(55, 67)(57, 65)(59, 66)(60, 71)(63, 68)(64, 72)(69, 70)
g1: (2, 4)(3, 6)(5, 9)(7, 11)(8, 13)(18, 21)(22, 28)(23, 26)(24, 30)(25, 27)(31, 35)(33, 34)(37, 39)(38, 41)(40, 44)(42, 47)(43, 49)(45, 52)(46, 54)(48, 57)(50, 60)(51, 62)(53, 64)(55, 59)(56, 65)(58, 67)(61, 69)(63, 70)(66, 71)(68, 72)
h1: (15, 29)
m1: (6, 35)

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

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