Signed graphs cospectral with the path

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Abstract

A signed graph Γ is said to be determined by its spectrum if every signed graph with the same spectrum as Γ is switching isomorphic with Γ. Here it is proved that the path Pn, interpreted as a signed graph, is determined by its spectrum if and only if n≡0,1, or 2 (mod 4), unless n∈{8,13,14,17,29}, or n=3.

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Akbari, S., Haemers, W. H., Maimani, H. R., & Parsaei Majd, L. (2018). Signed graphs cospectral with the path. Linear Algebra and Its Applications, 553, 104–116. https://doi.org/10.1016/j.laa.2018.04.021

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