On Betti numbers of edge ideals of crown graphs

摘要

An n-crown C_(n,n) on 2n vertices is a graph obtained from complete bipartite graph K_(n,n) by removing edges of a perfect matching. Given a finite simple graph G, one can associate a simplicial complex ?(G). In this paper, we use combinatorial data from the associated simplicial complex ?(C_(n,n)) of the crown graph C_(n,n) and give a formula to find Betti numbers of the form β_(i,i+1) of edge ideals of C_(n,n). We also present a formula to find a particular Betti of the edge ideal of a crown graph. We explicitly compute the projective dimension of the edge ideals of crown graphs using domination parameters of the graphs.