Quasi-Irreducibility of Nonnegative Biquadratic Tensors

Quasi-Irreducibility of Nonnegative Biquadratic Tensors

While the adjacency tensor of a bipartite 2-graph is a nonnegative biquadratic tensor, it is inherently reducible. To address this limitation, we introduce the concept of quasi-irreducibility in this paper. The adjacency tensor of a bipartite 2-graph is quasi-irreducible if that bipartite 2-graph is...

Full description

Saved in:
Bibliographic Details
Main Authors: Liqun Qi, Chunfeng Cui, Yi Xu
Format: Article
Language:English
Published: MDPI AG 2025-06-01
Series:Mathematics
Subjects:
nonnegative biquadratic tensors
bipartite 2-graphs
quasi-irreducibility
M<sup>0</sup>-eigenvalues
M<sup>++</sup>-eigenvalues
max-min theorem
Online Access:https://www.mdpi.com/2227-7390/13/13/2066
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:While the adjacency tensor of a bipartite 2-graph is a nonnegative biquadratic tensor, it is inherently reducible. To address this limitation, we introduce the concept of quasi-irreducibility in this paper. The adjacency tensor of a bipartite 2-graph is quasi-irreducible if that bipartite 2-graph is not bi-separable. This new concept reveals important spectral properties: although all M<sup>+</sup>-eigenvalues are M<sup>++</sup>-eigenvalues for irreducible nonnegative biquadratic tensors, the M<sup>+</sup>-eigenvalues of a quasi-irreducible nonnegative biquadratic tensor can be either M<sup>0</sup>-eigenvalues or M<sup>++</sup>-eigenvalues. Furthermore, we establish a max-min theorem for the M-spectral radius of a nonnegative biquadratic tensor.
ISSN:2227-7390

Similar Items