2023/03/27 by Hong‐Ying Lin, Bo Zhou, Lin, Hongying +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #Combinatorics (math.CO) #Electron Spin Resonance Studies #FOS: Mathematics #Phytoestrogen effects and research #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2303.14929
openalex publication_date 2023/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a k-uniform hypergraph G with vertex set [n] and edge set E(G), the ABC tensor ABC(G) of G is the k-order n-dimensional tensor with ABC(G)i1, …, ik= \begincases \dfrac1(k-1)!√[k]\dfrac∑i∈ edi-k∏i∈ edi amp; if e∈ E(G) 0 amp; otherwise \endcases for ij∈ [n] with j∈ [k], where di is the degree of vertex i in G. The ABC spectral radius of a uniform hypergraph is the spectral radius of its ABC tensor. We give tight lower and upper bounds for the ABC spectra radius, and determine the maximum ABC spectral radii of uniform hypertrees, uniform non-hyperstar hypertrees and uniform non-power hypertrees of given size, as well as the maximum ABC spectral radii of unicyclic uniform hypergraphs and linear unicyclic uniform hypergraphs of given size, respectively. We also characterize those uniform hypergraphs for which the maxima for the ABC spectral radii are actually attained in all cases.