On ABC spectral radius of uniform hypergraphs

Hongying Lin () and Bo Zhou ()
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Hongying Lin: South China University of Technology
Bo Zhou: South China Normal University

Journal of Combinatorial Optimization, 2024, vol. 47, issue 5, No 15, 44 pages

Abstract: Abstract Let G be a k-uniform hypergraph with vertex set [n] and edge set E(G), where $$k\ge 2$$ k ≥ 2 . For $$i\in [n]$$ i ∈ [ n ] , $$d_i$$ d i denotes the degree of vertex i in G. The ABC spectral radius of G is $$\begin{aligned} \max \left\{ k\sum _{e\in E(G)}\root k \of {\dfrac{\sum _{i\in e}d_{i} -k}{\prod _{i\in e}d_{i}}}\prod _{i\in e}x_i: \textbf{x}\in {\mathbb {R}}_+^n, \sum _{i=1}^nx_i^k=1\right\} . \end{aligned}$$ max k ∑ e ∈ E ( G ) ∑ i ∈ e d i - k ∏ i ∈ e d i k ∏ i ∈ e x i : x ∈ R + n , ∑ i = 1 n x i k = 1 . We give tight lower and upper bounds for the ABC spectral 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 uniform unicyclic hypergraphs and linear uniform unicyclic 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.

Keywords: ABC spectral radius; ABC tensor; Uniform hypergraphs; Extremal properties; 05C50; 05C65; 15A69 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10878-024-01182-2

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