A characterization of the Grassmann graphs: one missing case

TL;DR

This paper proves that Grassmann graphs of the form J_2(2D+3,D) for D≥3 are uniquely determined by their intersection numbers, resolving a previously open case in graph characterization.

Contribution

It establishes the characterization of a specific class of Grassmann graphs by their intersection numbers, completing the classification for this family.

Findings

Grassmann graphs J_2(2D+3,D) are characterized by intersection numbers

Resolved one of the last remaining open cases in graph characterization

Advances understanding of graph invariants in algebraic combinatorics

Abstract

We prove that the Grassmann graphs $J_2(2D+3,D)$, $D\geq 3$, are characterized by their intersection numbers, which settles one of the few remaining cases.