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On this page are computer-accessible forms for the graph C4[ 81, 5 ] = CPM(3,3,1,1).

(I) Following is a form readable by MAGMA:

g:=Graph<81|{ {36, 37}, {5, 7}, {64, 66}, {9, 11}, {1, 2}, {77, 78}, {61, 62}, {34, 38}, {72, 76}, {49, 53}, {42, 47}, {40, 47}, {56, 63}, {43, 44}, {4, 12}, {71, 79}, {54, 62}, {3, 10}, {50, 59}, {48, 57}, {17, 24}, {2, 8}, {16, 27}, {35, 40}, {37, 46}, {19, 31}, {53, 57}, {17, 28}, {52, 57}, {20, 25}, {34, 47}, {4, 10}, {1, 14}, {69, 74}, {33, 46}, {34, 45}, {14, 31}, {64, 81}, {4, 23}, {32, 52}, {4, 17}, {38, 48}, {46, 56}, {42, 60}, {41, 63}, {13, 26}, {32, 55}, {2, 26}, {5, 28}, {73, 80}, {39, 62}, {6, 31}, {15, 22}, {33, 59}, {45, 55}, {8, 19}, {39, 60}, {13, 17}, {13, 16}, {47, 50}, {78, 80}, {78, 81}, {9, 41}, {18, 50}, {29, 61}, {21, 52}, {22, 55}, {24, 58}, {26, 56}, {5, 38}, {18, 49}, {30, 58}, {31, 58}, {22, 48}, {12, 43}, {24, 63}, {21, 61}, {29, 53}, {30, 54}, {8, 33}, {9, 35}, {12, 38}, {1, 42}, {5, 41}, {9, 37}, {23, 59}, {13, 32}, {14, 35}, {6, 41}, {2, 51}, {20, 37}, {21, 36}, {26, 43}, {23, 36}, {30, 45}, {7, 51}, {28, 40}, {1, 52}, {25, 44}, {3, 53}, {27, 44}, {3, 58}, {7, 62}, {25, 34}, {27, 39}, {15, 49}, {6, 57}, {19, 44}, {7, 69}, {8, 74}, {14, 76}, {12, 72}, {15, 72}, {10, 66}, {24, 80}, {3, 74}, {6, 79}, {10, 67}, {11, 66}, {11, 71}, {11, 69}, {22, 70}, {23, 71}, {25, 73}, {28, 77}, {18, 65}, {27, 79}, {16, 70}, {29, 68}, {30, 68}, {16, 75}, {21, 73}, {18, 79}, {19, 78}, {29, 64}, {15, 81}, {20, 74}, {20, 75}, {33, 67}, {40, 75}, {39, 66}, {32, 71}, {55, 80}, {36, 76}, {46, 70}, {45, 69}, {42, 67}, {43, 64}, {54, 70}, {61, 77}, {35, 81}, {51, 65}, {48, 67}, {60, 73}, {50, 68}, {59, 77}, {49, 75}, {54, 76}, {51, 72}, {56, 68}, {60, 65}, {63, 65} }>;

(II) A more general form is to represent the graph as the orbit of {36, 37} under the group generated by the following permutations:

a: (2, 42)(4, 20)(5, 27)(7, 39)(8, 67)(9, 71)(10, 74)(12, 25)(13, 40)(14, 52)(15, 80)(16, 28)(17, 75)(18, 63)(19, 48)(21, 76)(22, 78)(23, 37)(24, 49)(26, 47)(29, 30)(31, 57)(32, 35)(34, 43)(38, 44)(41, 79)(45, 64)(46, 59)(50, 56)(51, 60)(53, 58)(54, 61)(55, 81)(66, 69)(70, 77)(72, 73)
b: (2, 42, 52, 14)(3, 62)(4, 77, 24, 5)(6, 72, 33, 73)(7, 10, 61, 58)(8, 60, 57, 76)(9, 43, 50, 55)(11, 64, 68, 45)(12, 59, 80, 41)(13, 40)(15, 46, 25, 79)(16, 75)(17, 28)(18, 22, 37, 44)(19, 65, 48, 36)(20, 27, 49, 70)(21, 31, 51, 67)(23, 78, 63, 38)(26, 47, 32, 35)(29, 30, 69, 66)(34, 71, 81, 56)(39, 53, 54, 74)
c: (1, 2, 51, 72, 76, 14)(3, 50, 17, 45, 75, 71)(4, 30, 40, 32, 74, 18)(5, 22, 37, 6, 67, 56)(7, 15, 36, 31, 42, 26)(8, 65, 12, 54, 35, 52)(9, 57, 33, 63, 38, 70)(10, 68, 28, 55, 20, 79)(11, 53, 59, 24, 34, 16)(13, 69, 49, 23, 58, 47)(19, 60, 43, 62, 81, 21)(25, 27, 66, 29, 77, 80)(39, 64, 61, 78, 73, 44)(41, 48, 46)
d: (4, 24)(6, 48)(9, 34)(10, 58)(11, 45)(12, 63)(14, 42)(15, 18)(19, 33)(22, 79)(23, 80)(25, 37)(27, 70)(30, 66)(31, 67)(35, 47)(36, 73)(38, 41)(39, 54)(43, 56)(44, 46)(50, 81)(55, 71)(59, 78)(60, 76)(64, 68)(65, 72)

(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[ 81, 5 ]
81
-1 2 14 52 42
-2 1 26 51 8
-3 58 74 53 10
-4 12 23 17 10
-5 38 28 7 41
-6 57 79 41 31
-7 69 5 51 62
-8 33 2 19 74
-9 11 35 37 41
-10 66 67 3 4
-11 66 69 71 9
-12 4 38 72 43
-13 26 16 17 32
-14 1 35 31 76
-15 22 81 49 72
-16 13 70 27 75
-17 13 24 4 28
-18 79 49 50 65
-19 44 78 8 31
-20 25 37 74 75
-21 36 61 73 52
-22 55 15 48 70
-23 36 4 59 71
-24 58 80 17 63
-25 44 34 73 20
-26 56 2 13 43
-27 44 79 16 39
-28 77 5 17 40
-29 68 61 53 64
-30 45 68 58 54
-31 14 58 6 19
-32 55 13 71 52
-33 67 46 59 8
-34 45 25 47 38
-35 14 81 40 9
-36 23 37 21 76
-37 46 36 9 20
-38 12 34 48 5
-39 66 27 60 62
-40 35 47 28 75
-41 5 6 63 9
-42 1 67 47 60
-43 44 12 26 64
-44 25 27 19 43
-45 55 34 69 30
-46 33 56 37 70
-47 34 50 40 42
-48 22 67 57 38
-49 15 18 53 75
-50 68 47 59 18
-51 2 72 7 65
-52 1 57 21 32
-53 57 3 49 29
-54 70 62 30 76
-55 22 45 80 32
-56 46 68 26 63
-57 48 6 52 53
-58 24 3 30 31
-59 33 77 23 50
-60 39 73 42 65
-61 77 29 62 21
-62 39 61 7 54
-63 56 24 41 65
-64 66 81 29 43
-65 60 18 51 63
-66 11 39 64 10
-67 33 48 42 10
-68 56 50 29 30
-69 11 45 7 74
-70 22 46 16 54
-71 11 23 79 32
-72 12 15 51 76
-73 25 80 60 21
-74 3 69 8 20
-75 16 49 40 20
-76 14 36 72 54
-77 78 59 28 61
-78 77 80 81 19
-79 27 71 6 18
-80 55 78 24 73
-81 78 35 15 64
0

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