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On this page are computer-accessible forms for the graph C4[ 68, 4 ] = R_34(19,18).

(I) Following is a form readable by MAGMA:

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

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

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

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

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