Note : you' ll need to run some stuff from bimodule - compatible - dimensions/SalemNumberTestFor11Families.nb

vinelistwithduals={{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1},{1},{1}}],DualData[{1},{1}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1},{1},{1}}],DualData[{1},{1}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1},{1}}],DualData[{1},{1},{1,2,3}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1},{1}}],DualData[{1},{1},{1,2,3}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1},{1}}],DualData[{1},{1},{3,2,1}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1},{1}}],DualData[{1},{1},{3,2,1}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1},{1}},{{1,1}}],DualData[{1},{1},{1}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1},{1}},{{1,1}}],DualData[{1},{1},{1}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1},{1}},{{1,0},{1,0},{0,1},{0,1}}],DualData[{1},{1},{4,2,3,1}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1},{1}},{{1,1}}],DualData[{1},{1},{1}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1},{1},{1}},{{1,0,0},{0,1,0}}],DualData[{1},{1},{1,2}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1},{1},{1}},{{1,0,0},{0,1,0}}],DualData[{1},{1},{1,2}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1},{1},{1}},{{1,0,0},{0,1,0}}],DualData[{1},{1},{2,1}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1},{1},{1}},{{1,0,0},{0,1,0}}],DualData[{1},{1},{2,1}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1},{1},{1}},{{1,0,0},{1,0,0}}],DualData[{1},{1},{1,2}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1},{1},{1}},{{1,0,0},{1,0,0}}],DualData[{1},{1},{1,2}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1},{1},{1}},{{1,0,0},{1,0,0}}],DualData[{1},{1},{2,1}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1},{1},{1}},{{1,0,0},{1,0,0}}],DualData[{1},{1},{1,2}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1},{1},{1}},{{1,0,0},{1,0,0}}],DualData[{1},{1},{2,1}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1},{1},{1}},{{1,0,0},{1,0,0}}],DualData[{1},{1},{2,1}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1},{1},{1}},{{1,0,0},{0,1,0},{0,0,1}}],DualData[{1},{1},{1,2,3}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1},{1},{1}},{{1,0,0},{0,1,0},{0,0,1}}],DualData[{1},{1},{1,2,3}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1},{1},{1}},{{1,0,0},{0,1,0},{0,0,1}}],DualData[{1},{1},{3,2,1}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1},{1},{1}},{{1,0,0},{0,1,0},{0,0,1}}],DualData[{1},{1},{3,2,1}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,1}}],DualData[{1},{1},{1,2}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,1}}],DualData[{1},{1},{1,2}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,1}}],DualData[{1},{1},{2,1}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,1}}],DualData[{1},{1},{2,1}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1},{1}},{{0,1,0},{0,1,0}}],DualData[{1},{1},{3,2,1}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1},{1}},{{0,1,0},{0,1,0}}],DualData[{1},{1},{3,2,1}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1},{1}},{{1,0,0},{0,0,1}}],DualData[{1},{1},{3,2,1}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1},{1}},{{1,0,0},{0,0,1}}],DualData[{1},{1},{3,2,1}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1},{1}},{{1,0,0},{0,1,0}}],DualData[{1},{1},{1,2,3}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1},{1}},{{1,0,0},{0,1,0}}],DualData[{1},{1},{1,2,3}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1},{1}},{{1,0,0},{1,0,0}}],DualData[{1},{1},{1,2,3}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1},{1}},{{1,0,0},{1,0,0}}],DualData[{1},{1},{1,2,3}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1},{1},{1}},{{1,0,0},{0,1,0}},{{1,0},{0,1}}],DualData[{1},{1},{2,1}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1},{1},{1}},{{1,0,0},{0,1,0}},{{1,0},{0,1}}],DualData[{1},{1},{2,1}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1},{1},{1}},{{1,0,0},{0,1,0}},{{1,0},{1,0}}],DualData[{1},{1},{1,2}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1},{1},{1}},{{1,0,0},{0,1,0}},{{1,0},{1,0}}],DualData[{1},{1},{1,2}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{0,1}},{{1,0},{0,1}}],DualData[{1},{1},{1,2},{2,1}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{1,0}}],DualData[{1},{1},{1,2}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{1,0}},{{1,0},{0,1}}],DualData[{1},{1},{1,2},{1,2}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{0,1}},{{1,1}}],DualData[{1},{1},{1,2},{1}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{1,0}},{{1,0},{1,0},{0,1}}],DualData[{1},{1},{1,2},{1,2,3}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{0,1}},{{1,1},{1,0}}],DualData[{1},{1},{1,2},{1,2}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{1,0}},{{1,0},{1,0},{0,1}}],DualData[{1},{1},{1,2},{2,1,3}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{0,1}},{{1,1},{1,0}}],DualData[{1},{1},{1,2},{1,2}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{1,0},{0,1}},{{1,0,0},{0,1,0},{0,0,1},{0,0,1}}],DualData[{1},{1},{1,2},{4,3,2,1}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{1,0},{1,0}}],DualData[{1},{1},{1,2}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1},{1}},{{1,0,0},{0,0,1}},{{1,0},{0,1}}],DualData[{1},{1},{3,2,1},{1,2}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1},{1}},{{0,1,0},{0,1,0}}],DualData[{1},{1},{3,2,1}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1},{1}},{{1,0,0},{0,0,1}},{{1,0},{0,1}}],DualData[{1},{1},{3,2,1},{2,1}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1},{1}},{{1,0,0},{0,0,1}},{{1,0},{0,1}}],DualData[{1},{1},{3,2,1},{2,1}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1},{1}},{{1,0,0},{0,1,0}},{{1,0},{0,1}}],DualData[{1},{1},{1,2,3},{1,2}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1},{1}},{{1,0,0},{0,1,0}},{{1,0},{0,1}}],DualData[{1},{1},{1,2,3},{1,2}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1},{1}},{{1,0,0},{0,1,0}},{{1,0},{0,1}}],DualData[{1},{1},{1,2,3},{2,1}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1},{1}},{{1,0,0},{1,0,0}}],DualData[{1},{1},{1,2,3}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1},{1}},{{1,0},{1,0},{0,1}},{{0,1,0},{0,0,1}},{{0,1}}],DualData[{1},{1},{3,2,1},{1}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1},{1}},{{1,0},{1,0},{0,1}},{{0,0,1},{0,1,0}},{{1,0}}],DualData[{1},{1},{3,2,1},{1}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1},{1},{1}},{{1,0,0},{0,1,0}},{{1,0},{0,1}},{{1,0},{0,1}}],DualData[{1},{1},{2,1},{2,1}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1},{1},{1}},{{1,0,0},{0,1,0}},{{1,0},{0,1}},{{1,0},{0,1}}],DualData[{1},{1},{2,1},{2,1}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{1,0}},{{1,0},{1,0},{0,1}},{{1,0,0}}],DualData[{1},{1},{1,2},{1,2,3}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{0,1}},{{1,1},{1,0}},{{0,1}}],DualData[{1},{1},{1,2},{1,2}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{1,0},{0,1}},{{1,0,0},{0,0,1}},{{0,1}}],DualData[{1},{1},{1,2},{2,1}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{0,1},{1,0}},{{1,0,0},{0,1,0}},{{0,1}}],DualData[{1},{1},{1,2},{2,1}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1},{1}},{{1,0},{1,0},{0,1}},{{0,1,0},{0,1,0},{0,0,1}},{{1,0,0},{0,0,1},{0,0,1}},{{0,0,1}}],DualData[{1},{1},{3,2,1},{3,2,1}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1},{1}},{{1,0},{1,0},{0,1}},{{0,1,0},{0,0,1},{0,1,0}},{{1,0,0},{0,1,0},{0,1,0}},{{0,0,1}}],DualData[{1},{1},{3,2,1},{3,2,1}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1},{1},{1}},{{1,0,0},{0,1,0}},{{1,0},{0,1}},{{1,0},{0,1}},{{1,0},{0,1}}],DualData[{1},{1},{2,1},{2,1}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1},{1},{1}},{{1,0,0},{0,1,0}},{{1,0},{0,1}},{{1,0},{0,1}},{{1,0},{0,1}}],DualData[{1},{1},{2,1},{2,1}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{0,1}},{{1,1}},{{1}},{{1}}],DualData[{1},{1},{1,2},{1},{1}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{1,0}},{{1,0},{0,1}},{{1,1}}],DualData[{1},{1},{1,2},{1,2}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{0,1}},{{1,0},{1,0},{0,1}},{{0,0,1}},{{1}}],DualData[{1},{1},{1,2},{3,2,1},{1}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{1,0}},{{1,0}},{{1}}],DualData[{1},{1},{1,2},{1}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{0,1}},{{1,0},{1,0},{0,1}},{{0,1,0},{0,1,0},{0,0,1}},{{1,0,0},{0,1,0},{0,0,1},{0,0,1},{0,0,1}}],DualData[{1},{1},{1,2},{3,2,1},{5,4,3,2,1}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{1,0}},{{1,0}},{{1},{1},{1}}],DualData[{1},{1},{1,2},{1}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{0,1}},{{1,0},{1,0},{1,0},{0,1}},{{0,0,0,1},{0,0,0,1}},{{1,0},{0,1}}],DualData[{1},{1},{1,2},{4,2,3,1},{1,2}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{1,0}},{{1,0},{1,0}},{{1,0},{0,1}}],DualData[{1},{1},{1,2},{1,2}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{0,1}},{{1,0},{1,0},{1,0},{0,1}},{{0,0,0,1},{0,0,0,1}},{{1,0},{0,1}}],DualData[{1},{1},{1,2},{4,2,3,1},{2,1}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{1,0}},{{1,0},{1,0}},{{1,0},{0,1}}],DualData[{1},{1},{1,2},{2,1}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{0,1}},{{1,0},{1,0},{1,0},{0,1}},{{0,0,0,1},{0,0,0,1}},{{1,0},{0,1}}],DualData[{1},{1},{1,2},{4,3,2,1},{1,2}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{1,0}},{{1,0},{1,0}},{{1,0},{0,1}}],DualData[{1},{1},{1,2},{1,2}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{0,1}},{{1,0},{1,0},{1,0},{0,1}},{{0,0,0,1},{0,0,0,1}},{{1,0},{0,1}}],DualData[{1},{1},{1,2},{4,3,2,1},{2,1}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{1,0}},{{1,0},{1,0}},{{1,0},{0,1}}],DualData[{1},{1},{1,2},{2,1}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{1,0}},{{1,0},{0,1}},{{1,0},{0,1}},{{1,1}}],DualData[{1},{1},{1,2},{1,2},{1}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{0,1}},{{1,0},{1,0},{0,1},{0,1}},{{0,0,0,1},{1,0,0,0}},{{1,0},{1,0},{0,1},{0,1}}],DualData[{1},{1},{1,2},{4,2,3,1},{1,2,3,4}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{1,0}},{{1,0},{0,1}},{{1,0},{0,1}},{{1,1}}],DualData[{1},{1},{1,2},{1,2},{1}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{0,1}},{{1,0},{1,0},{0,1},{0,1}},{{0,0,0,1},{1,0,0,0}},{{1,0},{1,0},{0,1},{0,1}}],DualData[{1},{1},{1,2},{4,2,3,1},{2,1,3,4}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{1,0}},{{1,0},{0,1}},{{1,0},{0,1}},{{1,1}}],DualData[{1},{1},{1,2},{1,2},{1}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{0,1}},{{1,0},{1,0},{0,1},{0,1}},{{0,0,0,1},{1,0,0,0}},{{1,0},{1,0},{0,1},{0,1}}],DualData[{1},{1},{1,2},{4,2,3,1},{2,1,4,3}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{1,0}},{{1,0},{0,1}},{{1,0},{0,1}},{{1,0},{1,0},{0,1},{0,1}}],DualData[{1},{1},{1,2},{1,2},{4,3,2,1}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{0,1}},{{1,0},{1,0},{0,1},{0,1}},{{0,0,0,1},{1,0,0,0}},{{1,1}}],DualData[{1},{1},{1,2},{4,2,3,1},{1}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{1,0}},{{1,0},{1,0},{0,1}},{{1,0,0}},{{1}}],DualData[{1},{1},{1,2},{1,2,3},{1}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{0,1}},{{1,1},{1,0}},{{0,1}},{{1}}],DualData[{1},{1},{1,2},{1,2},{1}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{0,1}},{{1,0},{1,0},{0,1},{0,1}},{{0,0,0,1},{1,0,0,0}},{{1,1}},{{1}},{{1}}],DualData[{1},{1},{1,2},{4,2,3,1},{1},{1}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{1,0}},{{1,0},{0,1}},{{1,0},{0,1}},{{1,0},{1,0},{0,1},{0,1}},{{1,0,0,1}}],DualData[{1},{1},{1,2},{1,2},{4,3,2,1}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{1,0}},{{1,0},{0,1}},{{1,0},{0,1}},{{1,1}},{{1}},{{1}}],DualData[{1},{1},{1,2},{1,2},{1},{1}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{0,1}},{{1,0},{1,0},{0,1},{0,1}},{{0,0,0,1},{1,0,0,0}},{{1,0},{1,0},{0,1},{0,1}},{{1,0,1,0}}],DualData[{1},{1},{1,2},{4,2,3,1},{1,2,3,4}]]},{BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{1,0},{0,1}},{{1,0,0},{0,1,0},{0,0,1}},{{0,1,0},{0,0,1}},{{1,0},{0,1}},{{0,1}},{{1}}],DualData[{1},{1},{1,2},{3,2,1},{2,1},{1}]],BigraphWithDuals[GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{0,1},{1,0}},{{1,0,0},{0,1,0},{0,1,0}},{{1,0,0},{0,0,1}},{{1,0}},{{1}}],DualData[{1},{1},{1,2},{3,2,1},{1}]]}};

DisplayBigraph/@vinelistwithduals

vinelist=Union[CanonicalizeBigraph/@Flatten[vinelistwithduals[[All,All,1]]]];

principalvinelist=Union[CanonicalizeBigraph/@Flatten[vinelistwithduals[[All,1,1]]]];

Length[principalvinelist]

DisplayBigraph /@ principalvinelist

goodprincipalvinelist=Select[principalvinelist,TestAForm]

badprincipalvinelist=Complement[principalvinelist,goodprincipalvinelist]

Nlist={{GradedBigraph[{{1}},{{1}},{{1},{1},{1}}],76},{GradedBigraph[{{1}},{{1}},{{1},{1}},{{1,1}}],75},{GradedBigraph[{{1}},{{1}},{{1},{1}},{{1,0},{1,0},{0,1},{0,1}}],94},{GradedBigraph[{{1}},{{1}},{{1},{1},{1}},{{0,0,1},{0,0,1}}],119},{GradedBigraph[{{1}},{{1}},{{1},{1},{1}},{{0,1,0},{0,0,1}}],94},{GradedBigraph[{{1}},{{1}},{{1},{1},{1}},{{0,1,0},{0,0,1}},{{1,0},{0,1}}],65},{GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{0,1},{0,1}},{{1,0},{0,1}}],87},{GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{0,1},{0,1}},{{0,1},{0,1},{1,0}}],87},{GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{0,1}},{{1,0},{0,1}}],89},{GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{0,1},{0,1}},{{0,1,0},{0,0,1},{1,0,0},{1,0,0}}],69},{GradedBigraph[{{1}},{{1}},{{1},{1}},{{1,0},{0,1},{0,1}},{{1,0,0},{0,0,1}},{{1,0}}],79},{GradedBigraph[{{1}},{{1}},{{1},{1},{1}},{{0,1,0},{0,0,1}},{{1,0},{0,1}},{{1,0},{0,1}}],79},{GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{0,1},{0,1}},{{1,0},{0,1},{0,1}},{{0,0,1}}],92},{GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{0,1},{0,1}},{{1,0},{0,1}},{{1,0},{0,1}},{{1,1}}],83},{GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{0,1},{0,1}},{{1,0},{0,1}},{{1,0},{0,1}},{{1,0},{1,0},{0,1},{0,1}}],134},{GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{0,1}},{{1,1}},{{1}},{{1}}],52},{GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{0,1}},{{1,0},{0,1},{0,1}},{{1,0,0}},{{1}}],87},{GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{0,1},{0,1}},{{1,0,0},{0,1,0},{0,0,1}},{{1,0,0},{0,0,1}},{{0,1},{1,0}},{{0,1}},{{1}}],152}};

Nlist=Table[{goodprincipalvinelist[[j]],FindN[goodprincipalvinelist[[j]],False]},{j,1,Length[goodprincipalvinelist]}]

CyclotomicTestUpToBound[g_GradedBigraph,n_Integer]:=CyclotomicTestUpToBound[g,n]=Module[{m=n-GraphRank[g],j,passed={}},
DebugPrint["Checking cyclotomicity for ",DisplayBigraph[g]," up to ", n];
For[j=0,j≤m,j++,
If[Mod[j,5]==0,DebugPrint[j]];
If[CyclotomicTest[Translate[g,j]],passed=Union[passed,{Translate[g,j]}];];
];
passed
];

passedlist={GradedBigraph[{{1}},{{1}},{{1},{1},{1}}],GradedBigraph[{{1}},{{1}},{{1}},{{1},{1},{1}}],GradedBigraph[{{1}},{{1}},{{1},{1}},{{1,1}}],GradedBigraph[{{1}},{{1}},{{1},{1}},{{1,0},{1,0},{0,1},{0,1}}],GradedBigraph[{{1}},{{1}},{{1},{1},{1}},{{0,1,0},{0,0,1}}],GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,1}}],GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{1,0},{0,1},{0,1}}],GradedBigraph[{{1}},{{1}},{{1}},{{1},{1},{1}},{{0,0,1},{0,0,1}}],GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{0,1},{0,1}},{{1,0},{0,1}}],GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{0,1},{0,1}},{{0,1},{0,1},{1,0}}],GradedBigraph[{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{0,1}},{{1,0},{0,1}}],GradedBigraph[{{1}},{{1}},{{1}},{{1},{1},{1}},{{0,1,0},{0,0,1}},{{1,0},{0,1}}],GradedBigraph[{{1}},{{1}},{{1},{1}},{{1,0},{0,1},{0,1}},{{1,0,0},{0,0,1}},{{1,0}}],GradedBigraph[{{1}},{{1}},{{1}},{{1}},{{1}},{{1},{1}},{{0,1},{0,1}},{{1,0},{0,1}}],GradedBigraph[{{1}},{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{0,1},{0,1}},{{1,0,0},{0,0,1}},{{1,0}}],GradedBigraph[{{1}},{{1}},{{1}},{{1}},{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{0,1}},{{1,0},{0,1}}],GradedBigraph[{{1}},{{1}},{{1}},{{1}},{{1}},{{1},{1}},{{0,1},{0,1}},{{1,0},{0,1}},{{1,0},{0,1}},{{1,1}}],GradedBigraph[{{1}},{{1}},{{1}},{{1}},{{1}},{{1},{1}},{{0,1},{0,1}},{{1,0},{0,1}},{{1,0},{0,1}},{{1,0},{1,0},{0,1},{0,1}}],GradedBigraph[{{1}},{{1}},{{1}},{{1}},{{1}},{{1},{1}},{{1,0},{0,1}},{{1,0},{0,1},{0,1}},{{1,0,0}},{{1}}]};

SetDebugMode[True]

badprincipalvinelist

otherlist=Union[CanonicalizeBigraph/@Flatten[CyclotomicTestUpToBound[#,50]& /@ badprincipalvinelist]]

passedlist=Union[CanonicalizeBigraph/@Flatten[CyclotomicTestUpToBound[#[[1]],(*#[[2]]*)30]& /@ Nlist]]

DisplayBigraph/@passedlist

DisplayBigraph/@(hooray=Cases[passedlist,g_/;KnownObstructions[g]=={}])

DisplayBigraph/@FindGraphPartners[hooray[[2]]]

DisplayBigraph/@FindGraphPartners[hooray[[6]]]

DimensionOfGenerator/@hooray

Conclusion

All of the graphs coming from the vines at the end of articles/index5-1/code/classification.nb that a) have Pn eventually Salem  and b) pass the cyclotomic test are:

{,,,,,,,,,,,,,,,,,,}