Research ArticleNo Access

Certain algebraic invariants of edge ideals of join of graphs

Arvind Kumar

https://orcid.org/0000-0002-2144-0588

Department of Mathematics, Indian Institute of Technology Madras, Chennai 600036 India

E-mail Address: arvkumar11@gmail.com

Corresponding author.

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Rajiv Kumar

Department of Mathematics, The LNM Institute of Information Technology, Jaipur, Rajasthan 302031 India

E-mail Address: gargrajiv00@gmail.com

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, and

Rajib Sarkar

Department of Mathematics, Indian Institute of Technology Madras, Chennai 600036 India

E-mail Address: rajib.sarkar63@gmail.com

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https://doi.org/10.1142/S0219498821500997Cited by:6 (Source: Crossref)

Abstract

Let $G$ be a simple graph and $I (G)$ be its edge ideal. In this paper, we study the Castelnuovo–Mumford regularity of symbolic powers of edge ideals of join of graphs. As a consequence, we prove Minh’s conjecture for wheel graphs, complete multipartite graphs, and a subclass of co-chordal graphs. We obtain a class of graphs whose edge ideals have regularity three. By constructing graphs, we prove that the multiplicity of edge ideals of graphs is independent from the depth, dimension, regularity, and degree of $h$ -polynomial. Also, we demonstrate that the depth of edge ideals of graphs is independent from the regularity and degree of $h$ -polynomial by constructing graphs.

Communicated by T. H. Ha

Keywords:

AMSC: 13D02, 13F55, 05E40

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