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On this page are computer-accessible forms for the graph C4[ 72, 16 ] = PL(WH_12(3,0,1,7),[3^12,4^9]).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {36, 38} under the group generated by the following permutations:

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

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

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