The Edge-Isoperimetric Problem on Sierpinski Graphs: Final Resolution

TL;DR

This paper solves the edge-isoperimetric problem on Sierpinski graphs S(n,m), proving that initial lexicographic segments are optimal solutions for all parameters, thus completing a previously open problem.

Contribution

It provides a complete proof that initial lexicographic segments solve the edge-isoperimetric problem on generalized Sierpinski graphs S(n,m).

Findings

Initial segments of lexicographic order are solutions for all n,m.

The problem is fully resolved for the class of Sierpinski graphs.

The paper extends previous partial results to a final, comprehensive solution.

Abstract

This paper completes the project started in [10]; to solve the edge-isoperimetric problem on the (generalized and extended) Sierpinski graph, S(n,m). We prove that initial segments of lexicographic order are solutions of the EIP for all n,m.