Cohen-Macaulayness of a class of graphs versus the class of their complements

被引：4

作者：

Ashitha, T. ^{[1
]}

Asir, T. ^{[1
]}

Hoang, D. T. ^{[2
]}

Pournaki, M. R. ^{[3
]}

机构：

[1] Madurai Kamaraj Univ, Dept Math DDE, Madurai 625021, Tamil Nadu, India

[2] Hanoi Univ Sci & Technol, Sch Appl Math & Informat, 1 Dai Co Viet, Hanoi, Vietnam

[3] Sharif Univ Technol, Dept Math Sci, POB 11155-9415, Tehran, Iran

来源：

DISCRETE MATHEMATICS | 2021年 / 344卷 / 10期

关键词：

Well-covered graph; Cohen-Macaulay graph; Vertex-decomposable graph; Gorenstein graph;

D O I：

10.1016/j.disc.2021.112525

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let n >= 2 be an integer. The graph G(n) is obtained by letting all the elements of {0, ..., n - 1} to be the vertices and defining distinct vertices x and y to be adjacent if and only if gcd(x + y, n) = 1. In this paper, well-coveredness, Cohen-Macaulayness, vertex-decomposability and Gorensteinness of these graphs and their complements are characterized. These characterizations provide large classes of Cohen-Macaulay and non Cohen-Macaulay graphs. (C) 2021 Elsevier B.V. All rights reserved.

引用

页数：9

共 9 条

[1] REGULAR SUBGRAPHS OF ALMOST REGULAR GRAPHS [J].

ALON, N ;

FRIEDLAND, S ;

KALAI, G .

JOURNAL OF COMBINATORIAL THEORY SERIES B, 1984, 37 (01) :79-91

[2]

Bruns W., 1993, COHEN MACAULAY RINGS

[3]

Grimaldi R.P., 1990, Congr. Numer., V71, P95

[4] Distributive lattices, bipartite graphs and Alexander duality [J].

Herzog, J ;

Hibi, T .

JOURNAL OF ALGEBRAIC COMBINATORICS, 2005, 22 (03) :289-302

[5]

Herzog J, 2011, GRAD TEXTS MATH, V260, P3, DOI 10.1007/978-0-85729-106-6

[6] Cohen-Macaulayness of two classes of circulant graphs [J].

Hoang, D. T. ;

Maimani, H. R. ;

Mousivand, A. ;

Pournaki, M. R. .

JOURNAL OF ALGEBRAIC COMBINATORICS, 2021, 53 (03) :805-827

[7]

Stanley R.P., 1996, COMBINATORICS COMMUT, V41

[8]

Villarreal RH., 2015, MONOMIAL ALGEBRAS MO

[9]

West D.B., 2018, Introduction to Graph Theory, V2nd

← 1 →