Riordan graphs I : structural properties
Cheon, Gi-Sang and Jung, Ji-Hwan and Kitaev, Sergey and Mojallal, Seyed Ahmad (2019) Riordan graphs I : structural properties. Linear Algebra and its Applications, 579. pp. 89-135. ISSN 0024-3795 (https://doi.org/10.1016/j.laa.2019.05.033)
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Abstract
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.
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Item type: Article ID code: 68056 Dates: DateEvent15 October 2019Published30 May 2019Published Online27 May 2019AcceptedSubjects: Science > Mathematics > Electronic computers. Computer science Department: Faculty of Science > Computer and Information Sciences Depositing user: Pure Administrator Date deposited: 28 May 2019 10:47 Last modified: 08 Aug 2024 01:40 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/68056