Research ArticleNo Access

Symbolic defects of edge ideals of unicyclic graphs

Mousumi Mandal

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

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

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

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and

Dipak Kumar Pradhan

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

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

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https://doi.org/10.1142/S0219498823500998Cited by:1 (Source: Crossref)

Abstract

We introduce the concept of minimum edge cover for an induced subgraph in a graph. Let $G$ be a unicyclic graph with a unique odd cycle and $I = I (G)$ be its edge ideal. We compute the exact values of all symbolic defects of $I$ using the concept of minimum edge cover for an induced subgraph in a graph. We describe one method to find the quasi-polynomial associated with the symbolic defects of edge ideal $I$ . We classify the class of unicyclic graphs when some power of maximal ideal annihilates $I^{(s)} / I^{s}$ for any fixed $s$ . Also for those class of graphs, we compute the Hilbert function of the module $I^{(s)} / I^{s}$ for all $s .$

Communicated by T. H. Ha

Keywords:

AMSC: 13F20, O5C25

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