Distance spectral radius of uniform hypergraphs

Lin, Hongying; Zhou, Bo

doi:10.1016/j.laa.2016.06.011

Cited by 20 publications

(12 citation statements)

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“…2 , then recalling that T 2β (0, 1) is the unique hypertree with maximum distance spectral radius among k-uniform hypertrees with m edges [8] and noting that β(T 2β (0, 1)) = m+1 2 , we have T ∼ = T 2β (0, 1), as desired.…”

mentioning

confidence: 81%

“…The following lemma was stated in [8] for a connected uniform hypergraph. However, its proof applies to any connected hypergraph that is not necessarily uniform.…”

Section: Preliminariesmentioning

confidence: 99%

“…[17] studied a q-ary extension of the classical binary addressing problem of graphs which was originally posed by Graham and Pollak [5], and found a sharp lower bound for the minimum length of addressings in terms of distance eigenvalues of uniform hypertrees. Lin and Zhou [8] and Lin et al [10] studied the distance spectral radius of uniform hypergraphs and particularly, uniform hypertrees. Lin and Zhou [9] studied the distance spectral radius of uniform hypergraphs with cycles, and particularly, uniform unicyclic hypergraphs.…”

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confidence: 99%

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Extremal properties of the distance spectral radius of hypergraphs

Wang¹,

Zhou

2020

ELA

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The distance spectral radius of a connected hypergraph is the largest eigenvalue of its distance matrix. The unique hypertrees with minimum distance spectral radii are determined in the class of hypertrees of given diameter, in the class of hypertrees of given matching number, and in the class of non-hyperstar-like hypertrees, respectively. The unique hypergraphs with minimum and second minimum distance spectral radii are determined in the class of unicylic hypergraphs. The unique hypertree with maximum distance spectral radius is determined in the class of $k$-th power hypertrees of given matching number.

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mentioning

confidence: 81%

“…The following lemma was stated in [8] for a connected uniform hypergraph. However, its proof applies to any connected hypergraph that is not necessarily uniform.…”

Section: Preliminariesmentioning

confidence: 99%

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confidence: 99%

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Extremal properties of the distance spectral radius of hypergraphs

Wang¹,

Zhou

2020

ELA

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“…Hypergraph theory has found applications in chemistry [2][3][4][5][6][7], showing a higher accuracy of molecular structure, that is, the higher accuracy of the model and the greater diversity of the behavior of its invariants. As an important descriptor of molecular structures, the Wiener index of a graph has many applications as well [8][9][10][11][12][13].…”

Section: Obviously We Have W(h) � (1/2) U∈v(h) W H (U)mentioning

confidence: 99%

A New Method to Find the Wiener Index of Hypergraphs

Deng

2020

Discrete Dynamics in Nature and Society

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The Wiener index is defined as the summation of distances between all pairs of vertices in a graph or in a hypergraph. Both models—graph-theoretical and hypergraph-theoretical—are used in mathematical chemistry for quantitatively studying physical and chemical properties of classical and nonclassical organic compounds. In this paper, we consider relationships between hypertrees and trees and hypercycles and cycles with respect to their Wiener indices.

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“…There are many results about the distance eigenvalues of graphs, see [2,8,14,16,23]. Recently, some scholars paid attention to the distance eigenvalues of hypergraphs, see [9][10][11][12]15,18,[20][21][22]. In [1], Aouchiche and Hansen defined the distance (signless) Laplacian eigenvalues of ordinary graphs, and we refer to [3,6,7,19] for more results.…”

Section: Introductionmentioning

confidence: 99%

Distance (Signless) Laplacian Eigenvalues of $k$-uniform Hypergraphs

Liu

Wang

2022

Taiwanese J. Math.

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The distance (signless) Laplacian eigenvalues of a connected hypergraph are the eigenvalues of its distance (signless) Laplacian matrix. For all n-vertex k-uniform hypertrees, we determine the k-uniform hypertree with minimum second largest distance (signless) Laplacian eigenvalue. For all n-vertex k-uniform unicyclic hypergraphs, we obtain the k-uniform unicyclic hypergraph with minimum largest distance (signless) Laplacian eigenvalue, and the k-uniform unicyclic hypergraph with minimum second largest distance Laplacian eigenvalue.

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Distance spectral radius of uniform hypergraphs

Abstract: We study the effect of three types of graft transformations to increase or decrease the distance spectral radius of uniform hypergraphs, and we determined the unique k-uniform hypertrees with maximum, second maximum, minimum and second minimum distance spectral radius, respectively.

Cited by 20 publications

References 10 publications

Extremal properties of the distance spectral radius of hypergraphs

Extremal properties of the distance spectral radius of hypergraphs

A New Method to Find the Wiener Index of Hypergraphs

Distance (Signless) Laplacian Eigenvalues of $k$-uniform Hypergraphs

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