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On this page are computer-accessible forms for the graph C4[ 68, 1 ] = W(34, 2).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {2, 3} under the group generated by the following permutations:

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

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

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