Characterizing the signless Laplacian Z-spectral radius for uniform hypergraphs

Abstract

This paper investigates the Z -spectral radius of uniform hypergraphs. For k -uniform hypergraphs ( k ≥ 4 ), we prove that ρ Z ( Q ( G ) ) = Δ , offering exact solutions to large-scale instances. Further, we propose novel Brualdi-type bounds for the signless Laplacian Z -spectral radius in the 3-uniform case based on vertex degrees. These approaches also yield sharp bounds for the Z -spectral radius of adjacency tensors, thereby improving existing bounds. Numerical experiments demonstrate the validity of our results.