Enlarging a connected graph while keeping entropy and spectral radius: self-similarity techniques

TL;DR

This paper explores self-similar sequences of connected graphs, demonstrating how to construct them and showing that such sequences preserve both entropy and spectral radius across all graphs.

Contribution

It introduces methods for constructing self-similar graph sequences that maintain key spectral and entropy properties, advancing understanding of graph growth and invariants.

Findings

All graphs in a self-similar sequence share the same entropy.

All graphs in such a sequence have identical spectral radius.

The paper provides a framework for constructing these sequences.

Abstract

This work is about self-similar sequences of growing connected graphs. We explain how to construct such sequences and why they are important. We show for instance that all the connected graphs in a self-similar sequence have not only the same entropy, but also the same spectral radius.