Research ArticlesNo Access

Regularity of powers of edge ideals of product of graphs

S. Selvaraja

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

https://doi.org/10.1142/S0219498818501281Cited by:3 (Source: Crossref)

Abstract

In this paper, we study the Castelnuovo–Mumford regularity of powers of edge ideals of product of graphs. We find new upper bounds for $reg (I {(G * H)}^{s})$ $reg (I {(G * H)}^{s})$ for various classes of graphs $G$ $G$ and $H$ $H$ , where $G * H$ $G * H$ denotes the product of $G$ $G$ and $H$ $H$ , and $I (G * H)$ $I (G * H)$ denote the corresponding edge ideal. Using this result, we explicitly compute $reg (I {(G * H)}^{s})$ $reg (I {(G * H)}^{s})$ for several classes of graphs $G$ $G$ and $H$ $H$ . In particular, we also explicitly compute the regularity of powers of wheel graphs.

Communicated by T. H. Ha

Keywords:

AMSC: 13F20, 13D02, 05C25, 05C70

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