Determines formulas for various graph properties in infinite families of finite graphs, suggesting new methods for analysis.
In this paper, we determine precise formulas for the diameters, the number of perfect matchings, and the Tutte polynomials for an infinite family of finite graphs, namely the Schreier graphs of tree automaton groups, also called tree graph automata. This enables us to easily find the number of spanning trees, spanning forests, and an explicit expression for the chromatic polynomials. In the second part of the paper, we provide the precise values for the Wiener and Szeged index of any tree graph automaton.
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D'Angeli et al. (2026) studied this question.
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