Orthogonal symmetric matrices and joins of graphs

@article{Levene2022OrthogonalSM,
  title={Orthogonal symmetric matrices and joins of graphs},
  author={Rupert H. Levene and Polona Oblak and Helena {\vS}migoc},
  journal={Linear Algebra and its Applications},
  year={2022}
}

Paths are generically realisable

We show that every 0-1 multiplicity matrix for a simple graph G is generically realisable for G. In particular, every multiplicity matrix for a path is generically realisable. We use this result to

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