On the spectral radius of uniform weighted hypergraph

2022/02/27 by Rui Sun, Sun Rui, Sun, Rui +2
Mathematics · Medicine · #Combinatorics (math.CO) #FOS: Mathematics #Phytoestrogen effects and research #Tensor decomposition and applications #math.CO

paper · pdf · doi:10.48550/arxiv.2202.13272

arxiv created 2022/02/27 · openalex publication_date 2022/02/27 · arxiv updated 2022/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let ℚ_k,n be the set of the connected k-uniform weighted hypergraphs with n vertices, where k,n≥ 3. For a hypergraph G∈ ℚ_k,n, let A(G), L (G) and Q (G) be its adjacency tensor, Laplacian tensor and signless Laplacian tensor, respectively. The spectral radii of A(G) and Q (G) are investigated. Some basic properties of the H-eigenvalue, the H⁺-eigenvalue and the H⁺⁺-eigenvalue of A(G), L (G) and Q (G) are presented. Several lower and upper bounds of the H-eigenvalue, the H⁺-eigenvalue and the H⁺⁺-eigenvalue for A(G), L (G) and Q (G) are established. The largest H⁺-eigenvalue of L (G) and the smallest H⁺-eigenvalue of Q (G) are characterized. A relationship among the H-eigenvalues of L (G), Q (G) and A (G) is also given.

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