An upper bound on the algebraic connectivity of regular graphs

TL;DR

This paper establishes a new upper bound on the algebraic connectivity of regular graphs using advanced mathematical techniques, providing insights into the structure of strongly regular graphs that maximize connectivity.

Contribution

It introduces a novel upper bound on algebraic connectivity for regular graphs and characterizes strongly regular graphs achieving this maximum.

Findings

New upper bound on algebraic connectivity

Characterization of strongly regular graphs with maximum connectivity

Enhanced understanding of regular graph connectivity

Abstract

We derive a new upper bound on the algebraic connectivity of a regular graph using the Higman-Sims technique. Together with a new result on the connectivity of the neighbourhood graph of strongly regular graphs, our result gives a characterization of a class of strongly regular graphs that maximize the algebraic connectivity amongst regular graphs.