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arXiv · 2404.09396

Main $\mathbf{Q}$-eigenvalues of quasi-threshold graphs

Átila Jones·Vilmar Trevisan·Cybele T. M. Vinagre
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Abstract

In this note, we present a structural description of certain connected cographs having $k \geq 2$ main signless Laplacian eigenvalues. This result allows us to characterize the cographs which are quasi-threshold graphs with two main $\mathbf{Q}$-eigenvalues. In addition, we describe all the quasi-threshold graphs belonging to the subclass of generalized core-satellite graphs with $k \geq 2$ main $\mathbf{Q}$-eigenvalues.

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Átila Jones, Vilmar Trevisan, Cybele T. M. Vinagre. 2024-04-15. Main $\mathbf{Q}$-eigenvalues of quasi-threshold graphs. https://doi.org/10.1016/j.laa.2025.02.009

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