Intriguing sets in distance regular graphs

TL;DR

This paper constructs an infinite family of intriguing sets in certain distance-regular graphs, demonstrating their minimality under specific conditions, and explores their properties in the Grassmann Graph of planes.

Contribution

It introduces a new family of intriguing sets in Grassmann graphs, expanding understanding of their structure and minimal examples in high-dimensional cases.

Findings

Constructed an infinite family of intriguing sets in Grassmann graphs.

Proved these sets are the smallest possible for certain parameters.

Identified conditions under which the sets are minimal.

Abstract

We construct an infinite family of intriguing sets that are not tight in the Grassmann Graph of planes of PG$(n,q)$, $n\ge 5$ odd, and show that the members of the family are the smallest possible examples if $n\ge 9$ or $q\ge 25$.