Orthogonalisability of joins of graphs

Fuente: arXiv
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Bibliographic Details
Main Authors: Levene, Rupert H., Oblak, Polona, Šmigoc, Helena
Format: Preprint
Published: 2025
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_version_ 1866916793137758208
author Levene, Rupert H.
Oblak, Polona
Šmigoc, Helena
author_facet Levene, Rupert H.
Oblak, Polona
Šmigoc, Helena
contents A graph is said to be orthogonalisable if the set of real symmetric matrices whose off-diagonal pattern is prescribed by its edges contains an orthogonal matrix. We determine some necessary and some sufficient conditions on the sizes of the connected components of two graphs for their join to be orthogonalisable. In some cases, those conditions coincide, and we present several families of joins of graphs that are orthogonalisable.
format Preprint
id arxiv_https___arxiv_org_abs_2503_20582
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Orthogonalisability of joins of graphs
Levene, Rupert H.
Oblak, Polona
Šmigoc, Helena
Combinatorics
Spectral Theory
15B10, 15B57, 15A18, 05C50
A graph is said to be orthogonalisable if the set of real symmetric matrices whose off-diagonal pattern is prescribed by its edges contains an orthogonal matrix. We determine some necessary and some sufficient conditions on the sizes of the connected components of two graphs for their join to be orthogonalisable. In some cases, those conditions coincide, and we present several families of joins of graphs that are orthogonalisable.
title Orthogonalisability of joins of graphs
topic Combinatorics
Spectral Theory
15B10, 15B57, 15A18, 05C50
url https://arxiv.org/abs/2503.20582