Betti Numbers of Edge Ideals of Grimaldi Graphs and Their Complements

IF 1 3区数学 Q1 MATHEMATICS

Bulletin of the Malaysian Mathematical Sciences Society Pub Date : 2024-06-27 DOI:10.1007/s40840-024-01731-2

T. Ashitha, T. Asir, D. T. Hoang, M. R. Pournaki

引用次数: 0

Abstract

Let \(n\ge 2\) be an integer. The Grimaldi graph G(n) is defined by taking the elements of the set \(\{ 0, \ldots , n-1 \}\) as vertices. Two distinct vertices x and y are adjacent in G(n) if and only if \(\gcd (x+y, n) =1\). In this paper, we examine the Betti numbers of the edge ideals of these graphs and their complements.

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格里马尔迪图边缘理想的贝蒂数及其补数

让 \(n\ge 2\) 是一个整数。格里马尔迪图 G(n) 由集合 \(\{ 0, \ldots , n-1 \}\)的元素作为顶点定义。当且仅当\(\gcd (x+y, n) =1\) 时，两个不同的顶点 x 和 y 在 G(n) 中是相邻的。本文将研究这些图的边理想的贝蒂数及其补数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Bulletin of the Malaysian Mathematical Sciences Society 数学-数学

CiteScore

2.40

自引率

8.30%

发文量

176

审稿时长

3 months

期刊介绍： This journal publishes original research articles and expository survey articles in all branches of mathematics. Recent issues have included articles on such topics as Spectral synthesis for the operator space projective tensor product of C*-algebras; Topological structures on LA-semigroups; Implicit iteration methods for variational inequalities in Banach spaces; and The Quarter-Sweep Geometric Mean method for solving second kind linear fredholm integral equations.