# Symbolic powers of certain cover ideals of graphs

## TL;DR

This paper investigates the algebraic properties of symbolic powers of cover ideals in specific classes of graphs, providing explicit formulas for regularity, Hilbert series, and multiplicity.

## Contribution

It offers new explicit computations of regularity, Hilbert series, and multiplicity for symbolic powers of cover ideals in crown and complete multipartite graphs.

## Key findings

- Computed regularity and Hilbert series for these ideals.
- Derived formulas for multiplicity based on graph edges.
- Enhanced understanding of algebraic invariants in graph theory.

## Abstract

In this paper, we compute the regularity and Hilbert series of symbolic powers of the cover ideal of a graph $G$ when $G$ is either a crown graph or a complete multipartite graph. We also compute the multiplicity of symbolic powers of cover ideals in terms of the number of edges.