On the<i>α</i>-spectral radius of irregular uniform hypergraphs

Lin, Hongying; Guo, Haiyan; Zhou, Bo

doi:10.1080/03081087.2018.1502253

Cited by 21 publications

(10 citation statements)

References 16 publications

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“…Inspired by the innovating work of Nikiforov [17], Lin, Guo and Zhou [14] proposed corresponding notation of the convex linear combination A α (G) of D(G) and A(G), which is defined as…”

Section: Definition 13 ([21]mentioning

confidence: 99%

Lower bounds for the $\mathcal{A}_α$-spectral radius of uniform hypergraphs

Zhang¹,

Zhang²

2021

Preprint

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For 0 ≤ α < 1, the Aα-spectral radius of a k-uniform hypergraph G is defined to be the spectral radius of the tensor Aα(G) := αD(G) + (1 − α)A(G), where D(G) and A(G) are diagonal and the adjacency tensors of G respectively. This paper presents several lower bounds for the difference between the Aα-spectral radius and an average degree km n for a connected k-uniform hypergraph with n vertices and m edges, which may be considered as the measures of irregularity of G. Moreover, two lower bounds on the Aα-spectral radius are obtained in terms of the maximum and minimum degrees of a hypergraph.

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“…Inspired by the innovating work of Nikiforov [17], Lin, Guo and Zhou [14] proposed corresponding notation of the convex linear combination A α (G) of D(G) and A(G), which is defined as…”

Section: Definition 13 ([21]mentioning

confidence: 99%

Lower bounds for the $\mathcal{A}_α$-spectral radius of uniform hypergraphs

Zhang¹,

Zhang²

2021

Preprint

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“…For a connected irregular k-uniform hypergraph G with n vertices, maximum degree ∆ and diameter D, where 2 ≤ k < n, it was shown in [12] that for 0 ≤ α < 1,…”

Section: Upper Bounds For α-Spectral Radiusmentioning

confidence: 99%

“…Let G be a connected k-uniform hypergraph with n vertices, m edges, maximum degree ∆ and diameter D, where k ≥ 2. For 0 ≤ α < 1, let x be the maximum entry of the α-Perron vector of G. From [12], we have…”

Section: Upper Bounds For α-Spectral Radiusmentioning

confidence: 99%

“…For a uniform hypergraph G, bounds for the spectral radius ρ 0 (G) have been given in [1,13,15,30], and bounds for the signless Laplacian spectral radius 2ρ 1/2 (G) may be found in [6,13,23]. Recently, Lin et al [12] gave upper bounds for α-spectral radius of connected irregular k-uniform hypergraphs, extending some known bounds for ordinary graphs. Some hypergraph transformations have been proposed to investigate the change of the 0-spectral radius, and the unique hypergraphs that maximize or minimize the 0-spectral radius have been determined among some classes of uniform hypergraphs (especially for hypertrees), see, e.g., [3,5,7,18,25,26,29,32].…”

Section: Introductionmentioning

confidence: 99%

“…is the signless Laplacian tensor of G [22]. Motivated by work of Nikiforov [16] (see also [4,17]), Lin et al [12] proposed to study the convex linear combinations A α (G) of D(G) and A(G) defined by…”

Section: Introductionmentioning

confidence: 99%

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On the $α$-spectral radius of uniform hypergraphs

Guo,

Zhou

2018

Preprint

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For 0 ≤ α < 1 and a uniform hypergraph G, the α-spectral radius of G is the largest H-eigenvalue of αD(G) + (1 − α)A(G), where D(G) and A(G) are the diagonal tensor of degrees and the adjacency tensor of G, respectively. We give upper bounds for the α-spectral radius of a uniform hypergraph, propose some transformations that increase the α-spectral radius, and determine the unique hypergraphs with maximum α-spectral radius in some classes of uniform hypergraphs.

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