The stabilizing index and cyclic index of coalescence and Cartesian product of uniform hypergraphs

2020/02/26 by Yi-Zheng Fan, Fan, Yi-Zheng, Meng-Yu Tian +3 · 1 citation
Mathematics · Medicine · #05C65 #14M99 #Advanced Neuroimaging Techniques and Applications #Combinatorics (math.CO) #FOS: Mathematics #Primary 15A18 #Secondary 13P15 #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2002.11715

openalex publication_date 2020/02/26 · openalex created_date 2020/03/06 · openalex updated_date 2026/07/28

Abstract

Let G be connected uniform hypergraph and let A(G) be the adjacency tensor of G. The stabilizing index of G is the number of eigenvectors of A(G) associated with the spectral radius, and the cyclic index of G is the number of eigenvalues of A(G) with modulus equal to the spectral radius. Let G₁ \odot G₂ and G₁ \Box G₂ be the coalescence and Cartesian product of connected m-uniform hypergraphs G₁ and G₂ respectively. In this paper, we give explicit formulas for the the stabilizing indices and cyclic indices of G₁ \odot G₂ and G₁ \Box G₂ in terms of those of G₁ and G₂ or the invariant divisors of their incidence matrices over ℤ_m, respectively.

Citations

• Perron–Frobenius theorem for nonnegative multilinear forms and extensions
• The spectral symmetry of weakly irreducible nonnegative tensors and connected hypergraphs

Cited by

• Lexicographical ordering by spectral moments of bicyclic hypergraphs

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