Graded Betti numbers of crown edge ideals

Abstract

An n-crown ${\mathcal{C}}_{n,n}$ on 2n vertices is a graph obtained from complete bipartite graph ${\mathcal{K}}_{n,n}$ by removing edges of a perfect matching. Given a finite simple graph G, one can associate a simplicial complex $\Delta (G)$. In this article, we use combinatorial data from the associated simplicial complex $\Delta ({\mathcal{C}}_{n,n})$ of the crown graph ${\mathcal{C}}_{n,n}$ and give formulas to find all Betti numbers of edge ideals of ${\mathcal{C}}_{n,n}$.

Keywords:

• Edge ideals
• Betti numbers
• regularity
• projective dimension
• t-type subsets

2010 Mathematics Subject Classification:

• 13D02
• 13F55
• 05C69
• 05C99

Disclosure statement

No potential conflict of interest was reported by the authors.