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The complement of the path is determined by its spectrum. (English) Zbl 1015.05047

Summary: It is proved that a graph whose \((0,1)\)-adjacency matrix has the spectrum of \(\overline{P_n}\), the complement of the path on \(n\) vertices, must be \(\overline{P_n}\).

MSC:

05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
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References:

[1] Bondy, J. A., Basic graph theory: paths and circuits, (Graham, R. L.; Grötschel, M.; Lovász, L., Handbook of Combinatorics (1995), Elsevier: Elsevier Amsterdam), Chapter 1 · Zbl 0849.05044
[2] Cvetković, D.; Doob, M.; Sachs, H., Spectra of Graphs (1995), Johann Abrosius Barth Verlag: Johann Abrosius Barth Verlag Heidelberg · Zbl 0824.05046
[3] Cvetković, D.; Rowlinson, P.; Simić, S., Eigenspaces of Graphs, (Encyclopedia of Mathematics and its Applications, vol. 66 (1997), Cambridge University Press: Cambridge University Press Cambridge) · Zbl 0878.05057
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