The α-spectral radius of general hypergraphs

Hongying Lin and Bo Zhou

Applied Mathematics and Computation, 2020, vol. 386, issue C

Abstract: Given a hypergraph H of order n with rank k ≥ 2, denote by D(H) and A(H) the degree diagonal tensor and the adjacency tensor of H, respectively, of order k and dimension n. For real number α with 0 ≤ α < 1, the α-spectral radius of H is defined to be the spectral radius of the symmetric tensor αD(H)+(1−α)A(H). First, we establish a upper bound on the α-spectral radius of connected irregular hypergraphs. Then we propose three local transformations of hypergraphs that increase the α-spectral radius. We also identify the unique hypertree with the largest α-spectral radius and the unique hypergraph with the largest α-spectral radius among hypergraphs of given number of pendent edges, and discuss the unique hypertrees with the next largest α-spectral radius and the unicyclic hypergraphs with the largest α-spectral radius.

Keywords: Hypergraph; Adjacency tensor; α-Spectral radius; Hypertrees; Unicyclic hypergraphs; Pendent edge (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:386:y:2020:i:c:s0096300320304100

DOI: 10.1016/j.amc.2020.125449

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