Algebraic Properties of Edge Ideals and Cover Ideals of Unbalanced Crown Graphs

In this paper, we introduce the unbalanced crown graphs Cm,n, and compute all graded Betti numbers of edge ideals of these graphs in terms of associated numerical data. As a consequence, we determine the regularity and the projective dimension of edge ideals of these graphs. Also, the Hilbert series of the cover ideals of these graphs is obtained.