### 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.

Language | English |
---|---|

Pages | 174-215 |

Number of pages | 42 |

Journal | Linear Algebra and its Applications |

Volume | 575 |

Early online date | 12 Apr 2019 |

DOIs | |

Publication status | Published - 15 Aug 2019 |

### Fingerprint

### Keywords

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

### Cite this

*Linear Algebra and its Applications*,

*575*, 174-215. https://doi.org/10.1016/j.laa.2019.04.011

}

*Linear Algebra and its Applications*, vol. 575, pp. 174-215. https://doi.org/10.1016/j.laa.2019.04.011

**Riordan graphs II : spectral properties.** / Cheon, Gi-Sang; Jung, Ji-Hwan; Kitaev, Sergey; Mojallal, Seyed Ahmad.

Research output: Contribution to journal › Article

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

PY - 2019/8/15

Y1 - 2019/8/15

N2 - 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.

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.

KW - Riordan graph

KW - adjacency eigenvalue

KW - Laplacian eigenvalue

KW - signless Laplacian eigenvalue

KW - intertia

KW - nullity

KW - Rayleigh-Ritz quotient

KW - Pascal graph

KW - Catalan graph

UR - https://www.sciencedirect.com/journal/linear-algebra-and-its-applications

UR - https://arxiv.org/abs/1801.07021

U2 - 10.1016/j.laa.2019.04.011

DO - 10.1016/j.laa.2019.04.011

M3 - Article

VL - 575

SP - 174

EP - 215

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

SN - 0024-3795

ER -