Betti numbers of some circulant graphs

Mohsen Abdi Makvand; Amir Mousivand

Czechoslovak Mathematical Journal (2019)

  • Volume: 69, Issue: 3, page 593-607
  • ISSN: 0011-4642

Abstract

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Let o ( n ) be the greatest odd integer less than or equal to n . In this paper we provide explicit formulae to compute ℕ -graded Betti numbers of the circulant graphs C 2 n ( 1 , 2 , 3 , 5 , ... , o ( n ) ) . We do this by showing that this graph is the product (or join) of the cycle C n by itself, and computing Betti numbers of C n * C n . We also discuss whether such a graph (more generally, G * H ) is well-covered, Cohen-Macaulay, sequentially Cohen-Macaulay, Buchsbaum, or S 2 .

How to cite

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Abdi Makvand, Mohsen, and Mousivand, Amir. "Betti numbers of some circulant graphs." Czechoslovak Mathematical Journal 69.3 (2019): 593-607. <http://eudml.org/doc/294601>.

@article{AbdiMakvand2019,
abstract = {Let $o(n)$ be the greatest odd integer less than or equal to $n$. In this paper we provide explicit formulae to compute $\mathbb \{N\}$-graded Betti numbers of the circulant graphs $C_\{2n\}(1,2,3,5,\ldots ,o(n))$. We do this by showing that this graph is the product (or join) of the cycle $C_n$ by itself, and computing Betti numbers of $C_n*C_n$. We also discuss whether such a graph (more generally, $G*H$) is well-covered, Cohen-Macaulay, sequentially Cohen-Macaulay, Buchsbaum, or $S_2$.},
author = {Abdi Makvand, Mohsen, Mousivand, Amir},
journal = {Czechoslovak Mathematical Journal},
keywords = {Betti number; Castelnuovo-Mumford regularity; projective dimension; circulant graph},
language = {eng},
number = {3},
pages = {593-607},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Betti numbers of some circulant graphs},
url = {http://eudml.org/doc/294601},
volume = {69},
year = {2019},
}

TY - JOUR
AU - Abdi Makvand, Mohsen
AU - Mousivand, Amir
TI - Betti numbers of some circulant graphs
JO - Czechoslovak Mathematical Journal
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 3
SP - 593
EP - 607
AB - Let $o(n)$ be the greatest odd integer less than or equal to $n$. In this paper we provide explicit formulae to compute $\mathbb {N}$-graded Betti numbers of the circulant graphs $C_{2n}(1,2,3,5,\ldots ,o(n))$. We do this by showing that this graph is the product (or join) of the cycle $C_n$ by itself, and computing Betti numbers of $C_n*C_n$. We also discuss whether such a graph (more generally, $G*H$) is well-covered, Cohen-Macaulay, sequentially Cohen-Macaulay, Buchsbaum, or $S_2$.
LA - eng
KW - Betti number; Castelnuovo-Mumford regularity; projective dimension; circulant graph
UR - http://eudml.org/doc/294601
ER -

References

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