The spectra of uniform hypertrees. (English) Zbl 1371.05168
Summary: In this paper we study the spectra of uniform hypertrees by using the generalized weighted incident matrix. We show that \(\lambda\) is a nonzero eigenvalue of the hypertree \(H\) corresponding to an eigenvector with all elements nonzero if and only if \(\lambda\) is a root of the polynomial \(\varphi(H) = \sum_{i = 0}^m(- 1)^i | \mathcal{M}_i | x^{(m - i) r}\), where \(| \mathcal{M}_i |\) is the number of matchings of order \(i\) in \(H\).
MSC:
| 05C50 | Graphs and linear algebra (matrices, eigenvalues, etc.) |
| 05C65 | Hypergraphs |
| 05C35 | Extremal problems in graph theory |
Keywords:
uniform hypergraph; spectrum; matching; hypertree; adjacency tensor; characteristic polynomialReferences:
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