The spectrum of a class of uniform hypergraphs

Kauê Cardoso; Carlos Hoppen; Vilmar Trevisan

doi:10.1016/j.laa.2019.12.042

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arXiv · 1909.00234

The spectrum of a class of uniform hypergraphs

Kauê Cardoso·Carlos Hoppen·Vilmar Trevisan

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Abstract

A generalized power hypergraph $\mathcal{H}^k_s$ is obtained from a base hypergraph $\mathcal{H}$ by means of some simple edge-expansion operations. Kang, Liu, Qi and Yuan [8] proved that the nonzero eigenvalues of $\mathcal{H}$ give rise to nonzero eigenvalues of $\mathcal{H}^k_s$. In this paper we show that all nonzero eigenvalues of $\mathcal{H}^k_s$ may be computed from the eigenvalues of its base hypergraph $\mathcal{H}$ and of its subgraphs. To prove this, we derive spectral results about edge-expansion operations that may be interesting on their own sake.

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Kauê Cardoso, Carlos Hoppen, Vilmar Trevisan. 2019-08-31. The spectrum of a class of uniform hypergraphs. https://doi.org/10.1016/j.laa.2019.12.042

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