The edge-isorperimetric problem on Sierpinski graphs

TL;DR

This paper explores how the recursive self-similar structure of graphs like Sierpinski gaskets can be utilized to prove isoperimetric theorems, advancing understanding of their geometric properties.

Contribution

It introduces a systematic method leveraging self-similarity to establish isoperimetric results on Sierpinski graphs, a novel approach in graph theory.

Findings

Established isoperimetric inequalities for Sierpinski graphs

Demonstrated the utility of recursive structures in geometric proofs

Provided a framework applicable to other self-similar graphs

Abstract

Some families of graphs, such as the n-cubes and Sierpinski gaskets, are self-similar. In this paper we show how such recursive structure can be used systematically to prove isoperimetric theorems.