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Regularity of bicyclic graphs and their powers

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 11 Apr 2019Embargo end date: 01 Jan 2018 France, France, Belgium, France, France Publisher:World Scientific Pub Co Pte LtJournal:Journal of Algebra and Its Applications, volume 19, page 2,050,057 (issn: 0219-4988, eissn: 1793-6829,

Authors: Sepehr Jafari; Yairon Cid-Ruiz; Beatrice Picone; Navid Nemati; Navid Nemati;

doi: 10.1142/s0219498820500577 , 10.48550/arxiv.1802.07202 , 10.13140/rg.2.2.23903.76961

arXiv: http://arxiv.org/abs/1802.07202

handle: 1854/LU-8681008

Regularity of bicyclic graphs and their powers

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Abstract

Let [Formula: see text] be the edge ideal of a bicyclic graph [Formula: see text] with a dumbbell as the base graph. In this paper, we characterize the Castelnuovo–Mumford regularity of [Formula: see text] in terms of the induced matching number of [Formula: see text]. For the base case of this family of graphs, i.e. dumbbell graphs, we explicitly compute the induced matching number. Moreover, we prove that [Formula: see text], for all [Formula: see text], when [Formula: see text] is a dumbbell graph with a connecting path having no more than two vertices.

Countries

France, France, Belgium, France, France

Related Organizations

University of Tehran
Iran (Islamic Republic of)
Laboratoire d'informatique de Paris 6
France
University of Barcelona
Spain
National and Kapodistrian University of Athens
Greece
Sorbonne University
France

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Keywords

MONOMIAL IDEALS, Algebra and Number Theory, regularity, 13D02, 05C25, 05C38, 05E40, Applied Mathematics, INDUCED MATCHINGS, induced matching number, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), Lozin transformation, [MATH.MATH-AC] Mathematics [math]/Commutative Algebra [math.AC], Bicyclic graphs, Mathematics and Statistics, even-connection, ASYMPTOTIC-BEHAVIOR, FOS: Mathematics, EDGE IDEALS, edge ideals

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