Distance spectral radii of k-uniform bicyclic hypergraphs

Xiangxiang Liu, Ligong Wang

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Abstract

Let G be a connected hypergraph. The distance spectral radius of G is the largest eigenvalue of its distance matrix. The Wiener index of G is defined to be the sum of distances between every unordered pair of vertices of G. A connected k-uniform hypergraph G with n vertices and m edges is called bicyclic if n = m(k − 1) − 1. Firstly, we obtain a lower bound on the Wiener index of k-uniform bicyclic hypergraphs with n vertices. As an application, among all k-uniform bicyclic hypergraphs with n vertices, we determine the first four bicyclic hypergraphs with smallest distance spectral radii for k ≥ 4, and the bicyclic hypergraph with minimum distance spectral radius for k = 3.

Original languageEnglish
Pages (from-to)6190-6210
Number of pages21
JournalLinear and Multilinear Algebra
Volume70
Issue number21
DOIs
StatePublished - 2022

Keywords

  • 05C50
  • 05C65
  • Distance spectral radius
  • k-uniform bicyclic hypergraph
  • Wiener index

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