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Open AccessFeature PaperArticle

The Regularity of Some Families of Circulant Graphs

1
Departamento de Matemáticas, Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Mexico City 07300, Mexico
2
Department of Mathematics and Statistics, McMaster University, Hamilton, ON L8S 4L8, Canada
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(7), 657; https://doi.org/10.3390/math7070657
Received: 18 June 2019 / Revised: 17 July 2019 / Accepted: 18 July 2019 / Published: 22 July 2019
(This article belongs to the Special Issue Current Trends on Monomial and Binomial Ideals)
We compute the Castelnuovo–Mumford regularity of the edge ideals of two families of circulant graphs, which includes all cubic circulant graphs. A feature of our approach is to combine bounds on the regularity, the projective dimension, and the reduced Euler characteristic to derive an exact value for the regularity. View Full-Text
Keywords: circulant graphs; edge ideals; Castelnuovo–Mumford regularity; projective dimension circulant graphs; edge ideals; Castelnuovo–Mumford regularity; projective dimension
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Uribe-Paczka, M.E.; Van Tuyl, A. The Regularity of Some Families of Circulant Graphs. Mathematics 2019, 7, 657.

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