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On this page are computer-accessible forms for the graph C4[ 80, 28 ] = SS[80,5].

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {68, 69} under the group generated by the following permutations:

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

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

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