Algebraic Invariants of the Powers of Edge Ideals of Caterpillars and some Forests

Abstract

The purpose of this dissertation is to analyze various algebraic properties, including Stanley depth, depth, regularity, and the projective dimension of the quotient rings obtained from the powers of edge ideals corresponding to caterpillar trees or a forest comprising these trees. The study establishes lower and upper bounds for the Stanley depth, depth, and the projective dimension of these quotient rings. Furthermore, the precise values of the regularity for the above quotient rings are also given