On Laplacian Energy of r-Uniform Hypergraphs

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 d...

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Published inSymmetry (Basel) Vol. 15; no. 2; p. 382
Main Author Yalçın, N. Feyza
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.02.2023
Subjects
Eigenvalues
Energy
graph energy
Graph theory
Graphs
hypergraph
Laplacian matrix
Matrix representation
Symmetry
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Abstract 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.
AbstractList 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.
Author Yalçın, N. Feyza
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Cites_doi 10.1073/pnas.37.11.760
10.1007/978-3-642-99970-3
10.1007/s11766-999-0034-x
10.13001/ela.2020.5025
10.1016/0009-2614(72)85099-1
10.1007/s10587-014-0100-2
10.1038/s42005-021-00637-w
10.2307/2306658
10.1007/s10114-004-0332-4
10.3390/sym14122560
10.1016/j.disc.2014.02.017
10.1016/j.jmaa.2006.03.072
10.1016/S0012-365X(00)00290-9
10.1016/j.laa.2020.05.029
10.1016/j.laa.2020.01.012
10.3390/sym13010140
10.1016/j.laa.2016.12.022
10.1007/s11425-007-0126-0
10.1515/spma-2022-0166
10.3390/sym10110582
10.1016/j.laa.2022.04.018
10.3390/sym14071402
10.1016/j.laa.2022.09.004
10.1080/03081080290011692
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References Fan (ref_22) 1951; 37
Banerjee (ref_8) 2017; 518
Das (ref_18) 2014; 325
Banerjee (ref_10) 2021; 614
Nordhaus (ref_25) 1956; 63
Cerone (ref_20) 2007; 38
(ref_12) 2002; 50
Gutman (ref_4) 1972; 17
Saha (ref_14) 2022; 655
Li (ref_17) 2004; 20
Cardoso (ref_11) 2022; 648
ref_24
Cardoso (ref_23) 2022; 10
Nikiforov (ref_21) 2007; 326
Konstantinova (ref_1) 2001; 235
(ref_19) 2014; 64
Sarkar (ref_9) 2020; 603
Wang (ref_16) 2007; 50
ref_3
Cardoso (ref_13) 2020; 36
Gutman (ref_26) 1978; 103
ref_5
ref_7
Li (ref_15) 1999; 14
Young (ref_2) 2021; 4
ref_6
References_xml – volume: 37
  start-page: 760
  year: 1951
  ident: ref_22
  article-title: Maximum properties and inequalities for the eigenvalues of completely continuous operators
  publication-title: Natl. Acad. Sci.
  doi: 10.1073/pnas.37.11.760
  contributor:
    fullname: Fan
– ident: ref_24
  doi: 10.1007/978-3-642-99970-3
– volume: 14
  start-page: 259
  year: 1999
  ident: ref_15
  article-title: A simplified Brauer’s theorem on matrix eigenvalues
  publication-title: Appl. Math. J. Chin. Univ. Ser. B
  doi: 10.1007/s11766-999-0034-x
  contributor:
    fullname: Li
– volume: 36
  start-page: 293
  year: 2020
  ident: ref_13
  article-title: Energies of hypergraphs
  publication-title: Electron. J. Linear Algebra
  doi: 10.13001/ela.2020.5025
  contributor:
    fullname: Cardoso
– volume: 17
  start-page: 535
  year: 1972
  ident: ref_4
  article-title: Graph theory and molecular orbitals. Total π-electron energy of alternant hydrocarbons
  publication-title: Chem. Phys. Lett.
  doi: 10.1016/0009-2614(72)85099-1
  contributor:
    fullname: Gutman
– volume: 64
  start-page: 285
  year: 2014
  ident: ref_19
  article-title: Remark on inequalities for the Laplacian spread of graphs
  publication-title: Czechoslov. Math.
  doi: 10.1007/s10587-014-0100-2
– volume: 4
  start-page: 1
  year: 2021
  ident: ref_2
  article-title: Hypergraph reconstruction from network data
  publication-title: Commun. Phys.
  doi: 10.1038/s42005-021-00637-w
  contributor:
    fullname: Young
– volume: 63
  start-page: 175
  year: 1956
  ident: ref_25
  article-title: On complementary graphs
  publication-title: Am. Math. Mon.
  doi: 10.2307/2306658
  contributor:
    fullname: Nordhaus
– volume: 20
  start-page: 803
  year: 2004
  ident: ref_17
  article-title: Upper bounds for the Laplacian graph eigenvalues
  publication-title: Acta Math. Sin.
  doi: 10.1007/s10114-004-0332-4
  contributor:
    fullname: Li
– ident: ref_6
  doi: 10.3390/sym14122560
– volume: 325
  start-page: 52
  year: 2014
  ident: ref_18
  article-title: On Laplacian energy of graphs
  publication-title: Discret. Math.
  doi: 10.1016/j.disc.2014.02.017
  contributor:
    fullname: Das
– volume: 38
  start-page: 37
  year: 2007
  ident: ref_20
  article-title: A refinement of the Grüss inequality and applications
  publication-title: J. Math.
  contributor:
    fullname: Cerone
– volume: 326
  start-page: 1472
  year: 2007
  ident: ref_21
  article-title: The energy of graphs and matrices
  publication-title: J. Math. Anal. Appl.
  doi: 10.1016/j.jmaa.2006.03.072
  contributor:
    fullname: Nikiforov
– volume: 235
  start-page: 365
  year: 2001
  ident: ref_1
  article-title: Application of hypergraph theory in chemistry
  publication-title: Discret. Math.
  doi: 10.1016/S0012-365X(00)00290-9
  contributor:
    fullname: Konstantinova
– volume: 603
  start-page: 101
  year: 2020
  ident: ref_9
  article-title: Joins of hypergraphs and their spectra
  publication-title: Linear Algebra Appl.
  doi: 10.1016/j.laa.2020.05.029
  contributor:
    fullname: Sarkar
– volume: 614
  start-page: 82
  year: 2021
  ident: ref_10
  article-title: On the spectrum of hypergraph
  publication-title: Linear Algebra Appl.
  doi: 10.1016/j.laa.2020.01.012
  contributor:
    fullname: Banerjee
– ident: ref_5
  doi: 10.3390/sym13010140
– volume: 518
  start-page: 14
  year: 2017
  ident: ref_8
  article-title: Spectra of general hypergraphs
  publication-title: Linear Algebra Appl.
  doi: 10.1016/j.laa.2016.12.022
  contributor:
    fullname: Banerjee
– volume: 50
  start-page: 1755
  year: 2007
  ident: ref_16
  article-title: Several sharp upper bounds for the largest Laplacian eigenvalue of a graph
  publication-title: Sci. China Ser. A Math.
  doi: 10.1007/s11425-007-0126-0
  contributor:
    fullname: Wang
– volume: 10
  start-page: 327
  year: 2022
  ident: ref_23
  article-title: The signless Laplacian matrix of hypergraphs
  publication-title: Spec. Matrices
  doi: 10.1515/spma-2022-0166
  contributor:
    fullname: Cardoso
– ident: ref_7
  doi: 10.3390/sym10110582
– volume: 648
  start-page: 181
  year: 2022
  ident: ref_11
  article-title: Adjacency energy of hypergraphs
  publication-title: Linear Algebra Appl.
  doi: 10.1016/j.laa.2022.04.018
  contributor:
    fullname: Cardoso
– volume: 103
  start-page: 1
  year: 1978
  ident: ref_26
  article-title: The energy of a graph
  publication-title: Berlin Math.-Stat. Forschungszentrum
  contributor:
    fullname: Gutman
– ident: ref_3
  doi: 10.3390/sym14071402
– volume: 655
  start-page: 1
  year: 2022
  ident: ref_14
  article-title: On the Laplacian spectrum of k-uniform hypergraphs
  publication-title: Linear Algebra Appl.
  doi: 10.1016/j.laa.2022.09.004
  contributor:
    fullname: Saha
– volume: 50
  start-page: 1
  year: 2002
  ident: ref_12
  article-title: On the Laplacian eigenvalues and metric parameters of hypergraphs
  publication-title: Linear Multilinear Algebra
  doi: 10.1080/03081080290011692
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StartPage 382
SubjectTerms Eigenvalues
Energy
graph energy
Graph theory
Graphs
hypergraph
Laplacian matrix
Matrix representation
Symmetry
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Title On Laplacian Energy of r-Uniform Hypergraphs
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