English

Paths are generically realisable

Combinatorics 2021-03-09 v1 Spectral Theory

Abstract

We show that every 00-11 multiplicity matrix for a simple graph GG is generically realisable for GG. In particular, every multiplicity matrix for a path is generically realisable. We use this result to provide several families of joins of graphs that are realisable by a matrix with only two distinct eigenvalues.

Keywords

Cite

@article{arxiv.2103.04587,
  title  = {Paths are generically realisable},
  author = {Rupert H. Levene and Polona Oblak and Helena Šmigoc},
  journal= {arXiv preprint arXiv:2103.04587},
  year   = {2021}
}