Frontiers of Mathematics in China >

2018 , Vol. 13 >Issue 2: 301 - 312

DOI: https://doi.org/10.1007/s11464-017-0678-4

RESEARCH ARTICLE

Largest H-eigenvalue of uniform s-hypertrees

  • Yuan HOU , 1,2 ,
  • An CHANG , 1 ,
  • Lei ZHANG 1
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  • 1. Center for Discrete Mathematics and Theoretical Computer Science, Fuzhou University, Fuzhou 350000, China
  • 2. Department of Computer Engineering, Fuzhou University Zhicheng College, Fuzhou 350000, China

Received date: 26 Jul 2017

Accepted date: 31 Oct 2017

Published date: 28 Mar 2018

Copyright

2018 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature
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Abstract

The k-uniform s-hypertree G = (V,E) is an s-hypergraph, where 1≤s≤k −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(Δs/k).

Key words： Largest H-eigenvalue; spectral radius; adjacency tensor; hypertree

Cite this article

Yuan HOU , An CHANG , Lei ZHANG . Largest H-eigenvalue of uniform s-hypertrees[J]. Frontiers of Mathematics in China, 2018 , 13(2) : 301 -312 . DOI: 10.1007/s11464-017-0678-4

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