The critical group of the Kneser graph on $2$-subsets of an $n$-element set

TL;DR

This paper computes the critical group of the Kneser graph KG(n,2), providing insights into its algebraic structure by determining the Smith normal form of its Laplacian matrix.

Contribution

It explicitly calculates the critical group of KG(n,2), a problem previously unresolved, advancing understanding of algebraic properties of Kneser graphs.

Findings

Critical group of KG(n,2) explicitly determined

Smith normal form of the Laplacian matrix computed

Enhances algebraic understanding of Kneser graphs

Abstract

In this paper we compute the critical group of the Kneser graph $KG(n,2)$. This is equivalent to computing the Smith normal form of a Laplacian matrix of this graph.