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
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Riordan graphs I : structural properties. / Cheon, Gi-Sang; Jung, Ji-Hwan; Kitaev, Sergey; Mojallal, Seyed Ahmad.
In: Linear Algebra and its Applications, Vol. 579, 15.10.2019, p. 89-135.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 -