Binomial edge ideals of generalized block graphs

被引：3

作者：

Kumar, Arvind ^{[1
]}

机构：

[1] Indian Inst Technol Madras, Dept Math, Chennai 600036, Tamil Nadu, India

来源：

INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION | 2020年 / 30卷 / 08期

关键词：

Binomial edge ideal; Castelnuovo-Mumford regularity; generalized block graph; extremal Betti number; COHEN-MACAULAY; REGULARITY;

D O I：

10.1142/S0218196720500526

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We classify generalized block graphs whose binomial edge ideals admit a unique extremal Betti number. We prove that the Castelnuovo-Mumford regularity of binomial edge ideals of generalized block graphs is bounded below by m(G) + 1, where m(G) is the number of minimal cut sets of the graph G and obtain an improved upper bound for the regularity in terms of the number of maximal cliques and pendant vertices of G.

引用

页码：1537 / 1554

页数：18

共 50 条

[1] ON THE GENERALIZED BINOMIAL EDGE IDEALS OF GENERALIZED BLOCK GRAPHS
Chaudhry, Faryal
Irfan, Rida
[J]. MATHEMATICAL REPORTS, 2020, 22 (3-4): : 381 - 394
[2] On the binomial edge ideals of block graphs
Chaudhry, Faryal
Dokuyucu, Ahmet
Irfan, Rida
[J]. ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, 2016, 24 (02): : 149 - 158
[3] Generalized binomial edge ideals of bipartite graphs
Shen, Yi-Huang
Zhu, Guangjun
[J]. JOURNAL OF ALGEBRA, 2025, 662 : 167 - 213
[4] Regularity of binomial edge ideals of certain block graphs
Jayanthan, A. V.
Narayanan, N.
Rao, B. V. Raghavendra
[J]. PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2019, 129 (03):
[5] Regularity of binomial edge ideals of certain block graphs
A V Jayanthan
N Narayanan
B V Raghavendra Rao
[J]. Proceedings - Mathematical Sciences, 2019, 129
[6] Powers of generalized binomial edge ideals of path graphs
Shen, Yi-Huang
Zhu, Guangjun
[J]. INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 2024, 34 (05) : 779 - 806
[7] Krull dimension and regularity of binomial edge ideals of block graphs
Mascia, Carla
Rinaldo, Giancarlo
[J]. JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2020, 19 (07)
[8] On the extremal Betti numbers of binomial edge ideals of block graphs
Herzog, Juergen
Rinaldo, Giancarlo
[J]. ELECTRONIC JOURNAL OF COMBINATORICS, 2018, 25 (01):
[9] Binomial edge ideals of graphs
Madani, Sara Saeedi
Kiani, Dariush
[J]. ELECTRONIC JOURNAL OF COMBINATORICS, 2012, 19 (02):
[10] Generalized binomial edge ideals
Rauh, Johannes
[J]. ADVANCES IN APPLIED MATHEMATICS, 2013, 50 (03) : 409 - 414

← 1 2 3 4 5 →