Kemeny's constant and enumerating Braess edges in trees

TL;DR

This paper investigates how to identify edges in trees that affect Kemeny's constant, providing bounds and asymptotic results for their enumeration in various tree families.

Contribution

It introduces methods to enumerate Braess edges in trees and derives bounds and asymptotic behaviors for these edges in different tree structures.

Findings

Bounds on the number of Braess edges in trees

Asymptotic results for specific tree families

Identification of structural properties influencing Kemeny's constant

Abstract

We study the problem of enumerating Braess edges for Kemeny's constant in trees. We obtain bounds and asympotic results for the number of Braess edges in some families of trees.