Regularity of 3-Path Ideals of Trees and Unicyclic Graphs

Article Type

Research Article

Publication Title

Bulletin of the Malaysian Mathematical Sciences Society

Abstract

Let G be a simple graph and I3(G) be its 3-path ideal in the corresponding polynomial ring R. In this article, we prove that for an arbitrary graph G, reg (R/ I3(G)) is bounded below by 2 ν3(G) , where ν3(G) denotes the 3-path induced matching number of G. We give a class of graphs, namely trees for which the lower bound is attained. Also, for a unicyclic graph G, we show that reg (R/ I3(G)) ≤ 2 ν3(G) + 2 and provide an example that shows that the given upper bound is sharp.

DOI

10.1007/s40840-023-01596-x

Publication Date

1-1-2024

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