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On this page are computer-accessible forms for the graph C4[ 80, 14 ] = PX(5,4).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {16, 31} under the group generated by the following permutations:

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

(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.

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&Graph
C4[ 80, 14 ]
80
-1 17 18 73 65
-2 73 19 20 65
-3 22 66 74 21
-4 66 23 24 74
-5 67 25 26 75
-6 67 27 28 75
-7 68 29 30 76
-8 68 31 32 76
-9 77 69 17 18
-10 77 69 19 20
-11 22 78 70 21
-12 23 78 24 70
-13 79 25 26 71
-14 79 27 71 28
-15 80 72 29 30
-16 80 72 31 32
-17 33 1 34 9
-18 1 35 36 9
-19 2 37 38 10
-20 2 39 40 10
-21 11 3 41 42
-22 11 44 3 43
-23 12 45 46 4
-24 12 47 4 48
-25 33 34 13 5
-26 13 35 36 5
-27 14 37 38 6
-28 14 6 39 40
-29 15 7 41 42
-30 44 15 7 43
-31 45 46 16 8
-32 47 48 16 8
-33 25 49 17 50
-34 25 17 51 52
-35 26 18 53 54
-36 55 56 26 18
-37 57 58 27 19
-38 59 27 60 19
-39 28 61 62 20
-40 28 63 20 64
-41 49 50 29 21
-42 29 51 52 21
-43 22 30 53 54
-44 22 55 56 30
-45 23 57 58 31
-46 23 59 60 31
-47 24 61 62 32
-48 24 63 64 32
-49 33 66 41 65
-50 33 67 68 41
-51 34 69 70 42
-52 34 71 72 42
-53 35 73 74 43
-54 35 75 43 76
-55 44 77 78 36
-56 44 79 36 80
-57 66 45 37 65
-58 45 67 68 37
-59 46 69 70 38
-60 46 38 71 72
-61 47 39 73 74
-62 47 39 75 76
-63 77 78 48 40
-64 79 80 48 40
-65 1 2 57 49
-66 57 3 4 49
-67 58 5 6 50
-68 58 50 7 8
-69 59 51 9 10
-70 11 12 59 51
-71 13 14 60 52
-72 15 16 60 52
-73 1 2 61 53
-74 3 4 61 53
-75 5 6 62 54
-76 7 62 8 54
-77 55 63 9 10
-78 11 55 12 63
-79 56 13 14 64
-80 56 15 16 64
0

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