Paths are generically realisable
Combinatorics
2021-03-09 v1 Spectral Theory
Abstract
We show that every - multiplicity matrix for a simple graph is generically realisable for . 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}
}