Riordan graphs II: spectral properties

Gi-Sang Cheon, Ji-Hwan Jung, Sergey Kitaev, Seyed Ahmad Mojallal

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The authors of this paper have used the theory of Riordan matrices to introduce the notion of a Riordan graph in [3]. Riordan graphs are proved to have a number of interesting (fractal) properties, and they are a far-reaching generalization of the well known and well studied Pascal graphs and Toeplitz graphs, and also some other families of graphs. The main focus in [3] is the study of structural properties of families of Riordan graphs obtained from certain infinite Riordan graphs. In this paper, we use a number of results in [3] to study spectral properties of Riordan graphs. Our studies include, but are not limited to the spectral graph invariants for Riordan graphs such as the adjacency eigenvalues, (signless) Laplacian eigenvalues, nullity, positive and negative inertia indices, and rank. We also study determinants of Riordan graphs, in particular, giving results about determinants of Catalan graphs.

LanguageEnglish
Pages174-215
Number of pages42
JournalLinear Algebra and its Applications
Volume575
Early online date12 Apr 2019
DOIs
Publication statusPublished - 15 Aug 2019

Fingerprint

Spectral Properties
Fractals
Structural properties
Graph in graph theory
Determinant
Signless Laplacian
Laplacian Eigenvalues
Graph Invariants
Nullity
Pascal
Otto Toeplitz
Adjacency
Inertia
Structural Properties
Fractal
Eigenvalue

Keywords

  • Riordan graph
  • adjacency eigenvalue
  • Laplacian eigenvalue
  • signless Laplacian eigenvalue
  • intertia
  • nullity
  • Rayleigh-Ritz quotient
  • Pascal graph
  • Catalan graph

Cite this

Cheon, Gi-Sang ; Jung, Ji-Hwan ; Kitaev, Sergey ; Mojallal, Seyed Ahmad. / Riordan graphs II : spectral properties. In: Linear Algebra and its Applications. 2019 ; Vol. 575. pp. 174-215.
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Riordan graphs II : spectral properties. / Cheon, Gi-Sang; Jung, Ji-Hwan; Kitaev, Sergey; Mojallal, Seyed Ahmad.

In: Linear Algebra and its Applications, Vol. 575, 15.08.2019, p. 174-215.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Riordan graphs II

T2 - Linear Algebra and its Applications

AU - Cheon, Gi-Sang

AU - Jung, Ji-Hwan

AU - Kitaev, Sergey

AU - Mojallal, Seyed Ahmad

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AB - The authors of this paper have used the theory of Riordan matrices to introduce the notion of a Riordan graph in [3]. Riordan graphs are proved to have a number of interesting (fractal) properties, and they are a far-reaching generalization of the well known and well studied Pascal graphs and Toeplitz graphs, and also some other families of graphs. The main focus in [3] is the study of structural properties of families of Riordan graphs obtained from certain infinite Riordan graphs. In this paper, we use a number of results in [3] to study spectral properties of Riordan graphs. Our studies include, but are not limited to the spectral graph invariants for Riordan graphs such as the adjacency eigenvalues, (signless) Laplacian eigenvalues, nullity, positive and negative inertia indices, and rank. We also study determinants of Riordan graphs, in particular, giving results about determinants of Catalan graphs.

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