SCT graphs with exotic solutions -- finding graphs of small size with exotic solutions

i1 : needsPackage "Oscillators"

o1 = Oscillators

o1 : Package

i2 : needsPackage "NautyGraphs"

o2 = NautyGraphs

o2 : Package

i3 : Gstrs = generateGraphs(5, OnlyConnected => true, MinDegree => 2);

i4 : Gs = Gstrs/stringToGraph

o4 = {Graph{0 => {3, 4}   }, Graph{0 => {3, 4}      }, Graph{0 => {2, 4}   
            1 => {3, 4}            1 => {3, 4}               1 => {3, 4}   
            2 => {3, 4}            2 => {3, 4}               2 => {0, 4}   
            3 => {0, 1, 2}         3 => {0, 1, 2, 4}         3 => {1, 4}   
            4 => {0, 1, 2}         4 => {3, 0, 1, 2}         4 => {2, 0, 3,
     ------------------------------------------------------------------------
       }, Graph{0 => {2, 3}}, Graph{0 => {2, 3, 4}}, Graph{0 => {2, 3, 4}
                1 => {3, 4}         1 => {3, 4}            1 => {3, 4}   
                2 => {0, 4}         2 => {0, 4}            2 => {0, 4}   
                3 => {0, 1}         3 => {0, 1}            3 => {0, 1, 4}
     1}         4 => {2, 1}         4 => {2, 0, 1}         4 => {2, 0, 3,
     ------------------------------------------------------------------------
       }, Graph{0 => {2, 3, 4}   }, Graph{0 => {2, 3, 4}}, Graph{0 => {2, 3,
                1 => {3, 4}               1 => {2, 3, 4}         1 => {2, 3,
                2 => {0, 3, 4}            2 => {0, 1, 4}         2 => {0, 1,
                3 => {2, 0, 1, 4}         3 => {0, 1}            3 => {0, 1,
     1}         4 => {2, 0, 3, 1}         4 => {2, 0, 1}         4 => {2, 0,
     ------------------------------------------------------------------------
     4}   }, Graph{0 => {2, 3, 4}   }, Graph{0 => {1, 2, 3, 4}}}
     4}            1 => {2, 3, 4}            1 => {0, 2, 3, 4}
     4}            2 => {0, 1, 3, 4}         2 => {1, 0, 3, 4}
     4}            3 => {2, 0, 1, 4}         3 => {1, 0, 2, 4}
     1, 3}         4 => {2, 0, 1, 3}         4 => {1, 0, 2, 3}

o4 : List

i5 : printingPrecision = 3

o5 = 3

i6 : for G in Gs list showExoticSolutions G;
warning: some solutions are not regular: {36, 41, 42, 43, 47, 48, 50, 51, 53, 54, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 71, 74, 75, 76, 77, 79, 80, 82, 85, 86, 87, 88, 89, 90}
 -- .566s elapsed
warning: some solutions are not regular: {49, 50, 53, 56, 57, 58, 59, 60, 61, 62, 63, 64, 67, 68, 69, 70, 71, 72, 73, 75, 77, 78, 80, 82, 83, 84, 85, 86, 88, 91, 94, 95, 97}
 -- .577s elapsed
 -- .771s elapsed
 -- 1.04s elapsed
-- found extra exotic solutions for graph Graph{0 => {2, 3}} --
                                                1 => {3, 4}
                                                2 => {0, 4}
                                                3 => {0, 1}
                                                4 => {2, 1}
+-----+----+----+-----+-----+-----+-----+-----+
|1    |1   |1   |1    |0    |0    |0    |0    |
+-----+----+----+-----+-----+-----+-----+-----+
|-.809|.309|.309|-.809|-.588|.951 |-.951|.588 |
+-----+----+----+-----+-----+-----+-----+-----+
|-.809|.309|.309|-.809|.588 |-.951|.951 |-.588|
+-----+----+----+-----+-----+-----+-----+-----+
-- angles (in degrees), first angle is zero and omitted --
+---+---+---+---+
|0  |0  |0  |0  |
+---+---+---+---+
|216|72 |288|144|
+---+---+---+---+
|144|288|72 |216|
+---+---+---+---+
 -- 1.01s elapsed
 -- 1.1s elapsed
warning: some solutions are not regular: {28, 30, 35, 37, 38, 40, 43, 44, 46, 47, 48, 53, 59, 60, 61}
 -- 1.25s elapsed
warning: some solutions are not regular: {16, 17, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34}
 -- .962s elapsed
 -- 1.11s elapsed
warning: some solutions are not regular: {26, 27, 30, 31, 33}
 -- 1.14s elapsed
warning: some solutions are not regular: {38, 44, 46, 49, 52, 53, 63, 70, 74, 75, 76, 77}
 -- 1.09s elapsed