Self-similar dendrites with finite boundary and P-sprouts

TL;DR

This paper explores the relationship between self-similar dendrites with finite boundaries and their associated sprout graphs, revealing how the sprout determines the dendrite's topological and combinatorial properties.

Contribution

It introduces the concept of the sprout graph G for self-similar dendrites and shows that G encodes key topological and combinatorial features of the dendrite.

Findings

The sprout G is a finite acyclic bipartite graph.

G determines the combinatorial properties of the dendrite.

G encodes the topological structure of the dendrite.

Abstract

Each self-similar dendrite K with a finite self-similar boundary defines a finite acyclic edge-labeled bipartite graph G, called the sprout of K. The paper shows that the sprout G determines the combinatorial properties of the dendrite K and its topological structure.