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June 2020 Closed neighborhood ideal of a graph
Leila Sharifan, Somayeh Moradi
Rocky Mountain J. Math. 50(3): 1097-1107 (June 2020). DOI: 10.1216/rmj.2020.50.1097

Abstract

We introduce a family of squarefree monomial ideals associated to finite simple graphs, whose monomial generators correspond to closed neighborhoods of vertices of the underlying graph. Any such ideal is called the closed neighborhood ideal of the graph. We study some algebraic invariants of these ideals like Castelnuovo–Mumford regularity and projective dimension and present some combinatorial descriptions for these invariants in terms of graph invariants.

Citation

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Leila Sharifan. Somayeh Moradi. "Closed neighborhood ideal of a graph." Rocky Mountain J. Math. 50 (3) 1097 - 1107, June 2020. https://doi.org/10.1216/rmj.2020.50.1097

Information

Received: 4 June 2019; Revised: 6 January 2020; Accepted: 9 January 2020; Published: June 2020
First available in Project Euclid: 29 July 2020

zbMATH: 07235599
MathSciNet: MR4132629
Digital Object Identifier: 10.1216/rmj.2020.50.1097

Subjects:
Primary: 05E40, 13F55
Secondary: 05C69

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.50 • No. 3 • June 2020
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