Algebraic Invariants of Edge Ideals of Some Bristled Circulant Graphs

Abstract

The purpose of this dissertation is to analyze various algebraic invariants, including Stanley depth, depth, regularity, and the projective dimension of the quotient rings obtained from the bristled of some four and five regular circulent graph. The study establishes exact values for the depth, regularity, and the projective dimension of these quotient rings. Moreover we obtain a lower bound for stanley depth.