Classification of Graph Fractaloids

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.