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Frontiers of Mathematics in China

, Volume 13, Issue 2, pp 301–312 | Cite as

Largest H-eigenvalue of uniform s-hypertrees

  • Yuan Hou
  • An Chang
  • Lei Zhang
Research Article

Abstract

The k-uniform s-hypertree G = (V,E) is an s-hypergraph, where 1 ≤ sk - 1; and there exists a host tree T with vertex set V such that each edge of G induces a connected subtree of T. In this paper, some properties of uniform s-hypertrees are establised, as well as the upper and lower bounds on the largest H-eigenvalue of the adjacency tensor of k-uniform s-hypertrees in terms of the maximal degree Δ. Moreover, we also show that the gap between the maximum and the minimum values of the largest H-eigenvalue of k-uniform s-hypertrees is just Θ(Δ s/k ).

Keywords

Largest H-eigenvalue spectral radius adjacency tensor hypertree 

MSC

05C50 

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Notes

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 11471077).

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Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Center for Discrete Mathematics and Theoretical Computer ScienceFuzhou UniversityFuzhouChina
  2. 2.Department of Computer EngineeringFuzhou University Zhicheng CollegeFuzhouChina

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