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 provide several families of joins of graphs that are realisable by a matrix with only two dist...
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| Sprache: | eng |
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| Zusammenfassung: | 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 provide several families
of joins of graphs that are realisable by a matrix with only two distinct
eigenvalues. |
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| DOI: | 10.48550/arxiv.2103.04587 |