The first few unicyclic and bicyclic hypergraphs with largest spectral radii

Chen Ouyang, Liqun Qi, Xiying Yuan

Research output: Journal article publicationJournal articleAcademic researchpeer-review

14 Citations (Scopus)

Abstract

A connected k-uniform hypergraph with n vertices and m edges is called r-cyclic if n=m(k−1)−r+1. For r=1 or 2, the hypergraph is simply called unicyclic or bicyclic. In this paper we investigate hypergraphs that attain largest spectral radii among all simple connected k-uniform unicyclic and bicyclic hypergraphs. Specifically, by using some edge operations, the formula on power hypergraph eigenvalues, the weighted incidence matrix and a result on linear unicyclic hypergraphs, we determined the first five hypergraphs with largest spectral radius among all unicyclic hypergraphs and the first three over all bicyclic hypergraphs.
Original languageEnglish
Pages (from-to)141-162
Number of pages22
JournalLinear Algebra and Its Applications
Volume527
DOIs
Publication statusPublished - 15 Aug 2017

Keywords

  • Adjacency tensor
  • Bicyclic hypergraph
  • k-Uniform hypergraph
  • Spectral radius
  • Unicyclic hypergraph

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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