### Abstract

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

Pages | 89-135 |

Number of pages | 47 |

Journal | Linear Algebra and its Applications |

Volume | 579 |

Early online date | 30 May 2019 |

DOIs | |

Publication status | E-pub ahead of print - 30 May 2019 |

### Fingerprint

### Keywords

- Riordan matrix
- graph decomposition
- fractal
- Toeplitz graph
- Pascal graph
- Riordan graph

### Cite this

*Linear Algebra and its Applications*,

*579*, 89-135. https://doi.org/10.1016/j.laa.2019.05.033

}

*Linear Algebra and its Applications*, vol. 579, pp. 89-135. https://doi.org/10.1016/j.laa.2019.05.033

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - Riordan graphs I

T2 - Linear Algebra and its Applications

AU - Cheon, Gi-Sang

AU - Jung, Ji-Hwan

AU - Kitaev, Sergey

AU - Mojallal, Seyed Ahmad

PY - 2019/5/30

Y1 - 2019/5/30

N2 - In this paper, we use the theory of Riordan matrices to introduce the notion of a Riordan graph. The Riordan graphs are a far-reaching generalization of the well known and well studied Pascal graphs and Toeplitz graphs, and also some other fami- lies of graphs. The Riordan graphs are proved to have a number of interesting (fractal) properties, which can be useful in creating computer networks with certain desirable features, or in obtaining useful information when designing algorithms to compute values of graph invariants. The main focus in this paper is the study of structural properties of families of Riordan graphs obtained from infinite Riordan graphs, which includes a fundamental decomposition theorem and certain conditions on Riordan graphs to have an Eulerian trail/cycle or a Hamiltonian cycle. We will study spectral properties of the Riordan graphs in a follow up paper.

AB - In this paper, we use the theory of Riordan matrices to introduce the notion of a Riordan graph. The Riordan graphs are a far-reaching generalization of the well known and well studied Pascal graphs and Toeplitz graphs, and also some other fami- lies of graphs. The Riordan graphs are proved to have a number of interesting (fractal) properties, which can be useful in creating computer networks with certain desirable features, or in obtaining useful information when designing algorithms to compute values of graph invariants. The main focus in this paper is the study of structural properties of families of Riordan graphs obtained from infinite Riordan graphs, which includes a fundamental decomposition theorem and certain conditions on Riordan graphs to have an Eulerian trail/cycle or a Hamiltonian cycle. We will study spectral properties of the Riordan graphs in a follow up paper.

KW - Riordan matrix

KW - graph decomposition

KW - fractal

KW - Toeplitz graph

KW - Pascal graph

KW - Riordan graph

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

U2 - 10.1016/j.laa.2019.05.033

DO - 10.1016/j.laa.2019.05.033

M3 - Article

VL - 579

SP - 89

EP - 135

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

SN - 0024-3795

ER -