Cheeger constants, growth and spectrum of locally tessellating planar graphs

TL;DR

This paper explores how local geometric properties of planar graphs influence their global invariants like Cheeger constants, growth, and spectrum, with implications for spectral graph theory.

Contribution

It establishes new relationships between local curvature and global spectral and geometric properties of planar graphs.

Findings

Connections between combinatorial curvature and Cheeger constants

Bounds on exponential growth based on local geometry

Spectral implications for planar graph analysis

Abstract

In this article, we study relations between the local geometry of planar graphs (combinatorial curvature) and em global geometric invariants, namely the Cheeger constants and the exponential growth. We also discuss spectral applications.