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On this page are computer-accessible forms for the graph C4[ 78, 1 ] = W(39,2).

(I) Following is a form readable by MAGMA:

g:=Graph<78|{ {2, 3}, {76, 77}, {74, 75}, {72, 73}, {70, 71}, {68, 69}, {66, 67}, {64, 65}, {62, 63}, {60, 61}, {58, 59}, {56, 57}, {54, 55}, {52, 53}, {50, 51}, {48, 49}, {46, 47}, {44, 45}, {42, 43}, {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}, {1, 2}, {77, 78}, {73, 74}, {69, 70}, {65, 66}, {61, 62}, {57, 58}, {53, 54}, {49, 50}, {45, 46}, {41, 42}, {21, 22}, {17, 18}, {5, 6}, {9, 10}, {13, 14}, {25, 26}, {29, 30}, {33, 34}, {37, 38}, {3, 4}, {75, 76}, {67, 68}, {59, 60}, {51, 52}, {43, 44}, {19, 20}, {11, 12}, {27, 28}, {35, 36}, {7, 8}, {71, 72}, {55, 56}, {23, 24}, {39, 40}, {15, 16}, {47, 48}, {1, 39}, {17, 55}, {16, 54}, {8, 46}, {9, 47}, {24, 62}, {25, 63}, {1, 41}, {22, 62}, {21, 61}, {20, 60}, {19, 59}, {18, 58}, {17, 57}, {16, 56}, {2, 42}, {3, 43}, {4, 44}, {5, 45}, {6, 46}, {7, 47}, {23, 63}, {2, 40}, {22, 60}, {19, 57}, {18, 56}, {3, 41}, {6, 44}, {7, 45}, {23, 61}, {4, 42}, {21, 59}, {20, 58}, {5, 43}, {8, 48}, {15, 55}, {9, 49}, {10, 50}, {11, 51}, {12, 52}, {13, 53}, {14, 54}, {10, 48}, {15, 53}, {11, 49}, {14, 52}, {12, 50}, {13, 51}, {31, 32}, {1, 78}, {24, 64}, {25, 65}, {26, 66}, {27, 67}, {28, 68}, {29, 69}, {30, 70}, {31, 71}, {26, 64}, {27, 65}, {30, 68}, {31, 69}, {28, 66}, {29, 67}, {32, 70}, {33, 71}, {40, 78}, {32, 72}, {33, 73}, {34, 74}, {35, 75}, {36, 76}, {37, 77}, {38, 78}, {34, 72}, {35, 73}, {38, 76}, {39, 77}, {36, 74}, {37, 75}, {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:

a: (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, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78)
b: (14, 53)
c: (28, 67)
d: (21, 60)
e: (12, 51)
f: (9, 48)
g: (15, 54)
h: (5, 44)
m: (16, 55)
n1: (22, 61)
a1: (35, 74)
b1: (23, 62)
c1: (3, 42)
d1: (8, 47)
e1: (29, 68)
f1: (34, 73)
g1: (18, 57)
h1: (2, 41)
m1: (33, 72)
n2: (11, 50)
a2: (26, 65)
b2: (27, 66)
c2: (24, 63)
d2: (37, 76)
e2: (36, 75)
f2: (4, 43)
g2: (32, 71)
h2: (25, 64)
m2: (39, 78)
n3: (13, 52)
a3: (10, 49)
b3: (2, 39)(3, 38)(4, 37)(5, 36)(6, 35)(7, 34)(8, 33)(9, 32)(10, 31)(11, 30)(12, 29)(13, 28)(14, 27)(15, 26)(16, 25)(17, 24)(18, 23)(19, 22)(20, 21)(41, 78)(42, 77)(43, 76)(44, 75)(45, 74)(46, 73)(47, 72)(48, 71)(49, 70)(50, 69)(51, 68)(52, 67)(53, 66)(54, 65)(55, 64)(56, 63)(57, 62)(58, 61)(59, 60)
c3: (31, 70)
d3: (30, 69)
e3: (17, 56)
f3: (7, 46)
g3: (20, 59)
h3: (6, 45)
m3: (38, 77)

(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[ 78, 1 ]
78
-1 78 2 39 41
-2 1 3 40 42
-3 2 4 41 43
-4 44 3 5 42
-5 45 4 6 43
-6 44 46 5 7
-7 45 47 6 8
-8 46 48 7 9
-9 47 49 8 10
-10 11 48 50 9
-11 12 49 51 10
-12 11 13 50 52
-13 12 14 51 53
-14 13 15 52 54
-15 55 14 16 53
-16 56 15 17 54
-17 55 57 16 18
-18 56 58 17 19
-19 57 59 18 20
-20 58 60 19 21
-21 22 59 61 20
-22 23 60 62 21
-23 22 24 61 63
-24 23 25 62 64
-25 24 26 63 65
-26 66 25 27 64
-27 67 26 28 65
-28 66 68 27 29
-29 67 69 28 30
-30 68 70 29 31
-31 69 71 30 32
-32 33 70 72 31
-33 34 71 73 32
-34 33 35 72 74
-35 34 36 73 75
-36 35 37 74 76
-37 77 36 38 75
-38 78 37 39 76
-39 77 1 38 40
-40 78 2 39 41
-41 1 3 40 42
-42 2 4 41 43
-43 44 3 5 42
-44 45 4 6 43
-45 44 46 5 7
-46 45 47 6 8
-47 46 48 7 9
-48 47 49 8 10
-49 11 48 50 9
-50 12 49 51 10
-51 11 13 50 52
-52 12 14 51 53
-53 13 15 52 54
-54 55 14 16 53
-55 56 15 17 54
-56 55 57 16 18
-57 56 58 17 19
-58 57 59 18 20
-59 58 60 19 21
-60 22 59 61 20
-61 23 60 62 21
-62 22 24 61 63
-63 23 25 62 64
-64 24 26 63 65
-65 66 25 27 64
-66 67 26 28 65
-67 66 68 27 29
-68 67 69 28 30
-69 68 70 29 31
-70 69 71 30 32
-71 33 70 72 31
-72 34 71 73 32
-73 33 35 72 74
-74 34 36 73 75
-75 35 37 74 76
-76 77 36 38 75
-77 78 37 39 76
-78 77 1 38 40
0

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