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Research Article | Open Access

Some algebraic invariants of the edge ideals of perfect [ h , d ]-ary trees and some unicyclic graphs

Tazeen Ayesha, Muhammad Ishaq( )
Department of Mathematics, School of Natural Sciences, National University of Sciences and Technology, H-12, Islamabad, Pakistan
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Abstract

This article is mainly concerned with computations of some algebraic invariants of quotient rings of edge ideals of perfect [ h , d ]-ary trees and unicyclic graphs. We compute exact values of depth and Stanley depth and consequently projective dimension for above mentioned quotient rings, except for the one special case of unicyclic graph for which best possible bounds of Stanley depth are given.

Keywords

depthedge idealStanley depthprojective dimensionperfect [h, d]-ary treeunicyclic graph
CLC number: 05C38, 05E99, 13C15, 13F20

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AIMS Mathematics
Volume 8 Issue 5,
May 2023
Pages 10947-10977
DOI: 10.3934/math.2023555

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Ayesha T, Ishaq M. Some algebraic invariants of the edge ideals of perfect [ h , d ]-ary trees and some unicyclic graphs. AIMS Mathematics, 2023, 8(5): 10947-10977. https://doi.org/10.3934/math.2023555

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Received: 05 October 2022
Revised: 13 February 2023
Accepted: 20 February 2023
Published: 15 May 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)