Adjacency energy of hypergraphs

Cardoso, Kauê; Del-Vecchio, Renata R.; Portugal, Lucas; Trevisan, Vilmar

doi:10.1016/j.laa.2022.04.018

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2023

2024

Publication Types

Select...

Article3

Relationship

Self Cite0

Independent3

Authors

Journals

Cited by 3 publications

(1 citation statement)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is known, however, that to obtain eigenvalues of tensors has a high computational and theoretical cost. Perhaps for this reason, recently, some authors have renewed the interest to study the matrix representations of a hypergraph, as for example in [1,3,6,9,11,12].…”

Section: Introductionmentioning

confidence: 99%

Incidence Energy of k-Uniform Hypertrees

Fu,

Gao

2024

MATCH

View full text Add to dashboard Cite

For a square matrix M, its energy E(M) is the sum of its singular values. Let H be a k-uniform hypergraph, and let B(H) be the incidence matrix of H. The incidence energy BE(H) of H is the energy of B(H). Let T n,d be the set of k-uniform hypertrees of order n and size r with diameter 3 ≤ d ≤ r − 1. In this article, the k-uniform hypertrees with minimum incidence energy over T n,d are characterized. In addition, we have obtained the incidence energy of a hyperstar, and determined which hyperstar has the maximum and minimum incidence energy among all hyperstars with n vertices.

show abstract

Section: Introductionmentioning

confidence: 99%

Incidence Energy of k-Uniform Hypertrees

Fu,

Gao

2024

MATCH

View full text Add to dashboard Cite

show abstract

Scalable Tensor Methods for Nonuniform Hypergraphs

Aksoy,

Amburg,

Young

2024

SIAM Journal on Mathematics of Data Science

View full text Add to dashboard Cite

On Laplacian Energy of r-Uniform Hypergraphs

Yalçin

2023

Symmetry

View full text Add to dashboard Cite

The matrix representations of hypergraphs have been defined via hypermatrices initially. In recent studies, the Laplacian matrix of hypergraphs, a generalization of the Laplacian matrix, has been introduced. In this article, based on this definition, we derive bounds depending pair-degree, maximum degree, and the first Zagreb index for the greatest Laplacian eigenvalue and Laplacian energy of r-uniform hypergraphs and r-uniform regular hypergraphs. As a result of these bounds, Nordhaus–Gaddum type bounds are obtained for the Laplacian energy.

show abstract

Adjacency energy of hypergraphs

Cited by 3 publications

References 19 publications

Incidence Energy of k-Uniform Hypertrees

Incidence Energy of k-Uniform Hypertrees

Scalable Tensor Methods for Nonuniform Hypergraphs

On Laplacian Energy of r-Uniform Hypergraphs

Contact Info

Product

Resources

About