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On this page are computer-accessible forms for the graph C4[ 72, 17 ] = PL(WH_12(3,1,6,7),[4^9,6^6]).

(I) Following is a form readable by MAGMA:

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

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

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

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