Tightness of the weight-distribution bound for strongly regular polar graphs

TL;DR

This paper investigates the tightness of the weight-distribution bound for eigenvalues of strongly regular polar graphs, providing characterizations of optimal eigenfunctions and extending results to certain unitary polar graphs.

Contribution

It demonstrates the tightness of the weight-distribution bound for specific eigenvalues and characterizes the associated optimal eigenfunctions in strongly regular and some unitary polar graphs.

Findings

Proves tightness of the weight-distribution bound for positive eigenvalues.

Characterizes optimal eigenfunctions for strongly regular polar graphs.

Shows tightness of the bound for negative eigenvalues in some unitary polar graphs.

Abstract

In this paper we show the tightness of the weight-distribution bound for the positive non-principle eigenvalue of strongly regular (affine) polar graphs and characterise the optimal eigenfunctions. Additionally, we show the tightness of the weight-distribution bound for the negative non-principle eigenvalue of some unitary polar graphs.