Oriented Riordan graphs and their fractal property

TL;DR

This paper introduces oriented Riordan graphs, a generalization of Toeplitz oriented graphs and tournaments, exploring their structural properties, fractal nature, and a new class called p-Riordan graphs.

Contribution

It defines oriented Riordan graphs using Riordan matrices, proves their fundamental decomposition and fractal properties, and introduces p-Riordan graphs as a generalization.

Findings

Oriented Riordan graphs exhibit a fractal property.

A fundamental decomposition theorem for these graphs is established.

Introduction of p-Riordan graphs as a new generalization.

Abstract

In this paper, we use the theory of Riordan matrices to introduce the notion of an oriented Riordan graph. The oriented Riordan graphs are a far-reaching generalization of the well known and well studied Toeplitz oriented graphs and tournament. The main focus in this paper is the study of structural properties of the oriented Riordan graphs which includes a fundamental decomposition theorem and fractal property. Finally, we introduce the generalization of the oriented Riordan graph who is called a $p$-Riordan graph.