Least H-eigenvalue of adjacency tensor of hypergraphs with cut vertices

Abstract

Let G be a connected hypergraph with even uniformity, which contains cut vertices. Then G is the coalescence of two nontrivial connected sub-hypergraphs (called branches) at a cut vertex. Let \(\mathscr{A}(G)\) be the adjacency tensor of G. The least H-eigenvalue of \(\mathscr{A}(G)\) refers to the least real eigenvalue of \(\mathscr{A}(G)\) associated with a real eigenvector. In this paper, we obtain a perturbation result on the least H-eigenvalue of \(\mathscr{A}(G)\) when a branch of G attached at one vertex is relocated to another vertex, and characterize the unique hypergraph whose least H-eigenvalue attains the minimum among all hypergraphs in a certain class of hypergraphs which contain a fixed connected hypergraph.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11871073, 11771016).

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Correspondence to Yizheng Fan.

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Fan, Y., Zhu, Z. & Wang, Y. Least H-eigenvalue of adjacency tensor of hypergraphs with cut vertices. Front. Math. China 15, 451–465 (2020). https://doi.org/10.1007/s11464-020-0842-0

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Keywords

  • Hypergraph
  • adjacency tensor
  • least H-eigenvalue
  • eigenvector
  • perturbation

MSC

  • 15A18
  • 05C65
  • 13P15