Some algebraic invariants of the edge ideals of some $q$-fold bristled graphs

TL;DR

This paper calculates algebraic invariants such as regularity, depth, Stanley depth, and projective dimension for edge ideals of specific complex graphs, advancing understanding of their algebraic properties.

Contribution

It provides exact values of these invariants for edge ideals of multi triangular snake and ouroboros snake graphs, including their q-fold bristled variants, which was previously unexplored.

Findings

Exact regularity values for the quotient rings of the edge ideals.

Computed depth, Stanley depth, and projective dimension for these graph classes.

Enhanced understanding of algebraic invariants in complex graph structures.

Abstract

In this paper, we compute the exact values of regularity of the quotient rings of the edge ideals associated to multi triangular snake and multi triangular ouroboros snake graphs. Also we compute the exact values of depth, Stanley depth, regularity and projective dimension of the quotient rings of the edge ideals associated to $q$-fold bristled graphs of multi triangular snake and multi triangular ouroboros snake graphs.