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Invariants of the symbolic powers of edge ideals

Bidwan Chakraborty

Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur 721302, India

E-mail Address: bidwan@iitkgp.ac.in

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and

Mousumi Mandal

http://orcid.org/0000-0003-2068-8212

Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur 721302, India

E-mail Address: mousumi@maths.iitkgp.ac.in

Corresponding author.

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https://doi.org/10.1142/S0219498820501844Cited by:3 (Source: Crossref)

Abstract

Let $G$ $G$ be a graph and $I = I (G)$ $I = I (G)$ be its edge ideal. When $G$ $G$ is the clique sum of two different length odd cycles joined at single vertex then we give an explicit description of the symbolic powers of $I$ $I$ and compute the Waldschmidt constant. When $G$ $G$ is complete graph then we describe the generators of the symbolic powers of $I$ $I$ and compute the Waldschmidt constant and the resurgence of $I$ $I$ . Moreover for complete graph we prove that the Castelnuovo–Mumford regularity of the symbolic powers and ordinary powers of the edge ideal coincide.

Communicated by T. H. Ha

Keywords:

AMSC: 13D02, 13D05, 05C25, 05C38, 05E40, 13C15, 13D45

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