Some algebraic invariants of the edge ideals of perfect [h,d]-ary trees and some unicyclic graphs

Abstract

This article is mainly concerned with computations of some algebraic invariants of quotient rings of edge ideals of perfect [h,d]-ary trees and unicyclic graphs. We compute exact values of depth and Stanley depth and consequently projective dimension for above mentioned quotient rings, except for the one special case of unicyclic graph for which best possible bounds of Stanley depth are given.

Keywords

• depth
• edge ideal
• stanley depth
• projective dimension
• perfect [h，d]-ary tree
• unicyclic graph