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arXiv · 2503.20582

Orthogonalisability of joins of graphs

Rupert H. Levene·Polona Oblak·Helena Šmigoc
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Abstract

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.

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Rupert H. Levene, Polona Oblak, Helena Šmigoc. 2025-06-11. Orthogonalisability of joins of graphs. https://doi.org/10.1016/j.laa.2025.06.001

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