Classification of Graph Fractaloids

TL;DR

This paper introduces a classification method for graph fractaloids using spectral data from radial operators, defining a fractal pair that uniquely characterizes each fractaloid.

Contribution

It provides a novel classification framework for graph fractaloids based on spectral analysis and introduces the fractal pair concept for their categorization.

Findings

Graph fractaloids can be classified by spectral data.

The fractal pair $(N_0, N^0)$ uniquely identifies each fractaloid.

Spectral properties are key to understanding the structure of graph fractaloids.

Abstract

In this paper, we observe graph fractaloids, which are the graph groupoids with fractal property. In particular, we classify them in terms of the spectral data of certain Hilbert space operators, called the radial operators. Based on these information, we can define the pair of two numbers $(N_{0},$ $N^{0})$, for a given graph fractaloid G, called the fractal pair of G. The graph fractaloids are classified by such pairs.