Characterizing and computing weight-equitable partitions of graphs

TL;DR

This paper advances the understanding of weight-equitable partitions in graphs by exploring their spectral properties, algebraic characterizations, and proposing a method for finding coarse partitions.

Contribution

It introduces new spectral and algebraic insights into weight-equitable partitions and presents a computational method to identify coarse partitions.

Findings

Spectral properties of weight-equitable partitions analyzed

Algebraic characterizations developed

Method for finding coarse weight-equitable partitions proposed

Abstract

Weight-equitable partitions of graphs, which are a natural extension of the well-known equitable partitions, have been shown to be a powerful tool to weaken the regularity assumption in several well-known eigenvalue bounds. In this work we aim to further our algebraic and computational understanding of weight-equitable partitions. We do so by showing several spectral properties and algebraic characterizations, and by providing a method to find coarse weight-equitable partitions.