Sufficient conditions for optimally and super m-restricted edge-connected graphs with given girth

被引：0

作者：

Liu, Saihua ^{[1
]}

Ouyang, Chen ^{[2
]}

Ou, Jianping ^{[1
]}

机构：

[1] Wuyi Univ, Dept Math, Jiangmen, Peoples R China

[2] Dongguan Univ Technol, Sch Comp Sci & Technol, Dongguan 523000, Peoples R China

来源：

LINEAR & MULTILINEAR ALGEBRA | 2022年 / 70卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Girth; m-restricted edge connectivity; lambda(m)-optimal; super-lambda(m); CUTS LEAVING COMPONENTS; ORDER;

D O I：

10.1080/03081087.2020.1754749

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A -connected graph G is optimally m-restricted edge-connected if its m-restricted edge-connectivity equals the minimum m-edge-degree , and super m-restricted edge-connected if all minimum m-restricted edge cuts are trivial. In this study, a bound for the size of graphs with girth greater than any given integer l is obtained firstly. Then the second minimum degree conditions for optimally and super m-restricted edge-connected graphs with girth greater than l are provided. Furthermore, the relationship between optimally m-restricted edge connectivity and optimally -restricted edge connectivity is characterized.

引用

页码：1146 / 1158

页数：13

共 50 条

[41] Sufficient conditions on the zeroth-order general Randic index for maximally edge-connected graphs
Chen, Zhibing
Su, Guifu
Volkmann, Lutz
DISCRETE APPLIED MATHEMATICS, 2017, 218 : 64 - 70
[42] Optimally super-edge-connected transitive graphs
Meng, JX
DISCRETE MATHEMATICS, 2003, 260 (1-3) : 239 - 248
[43] Degree sequence conditions for maximally edge-connected and super-edge-connected oriented graphs depending on the clique number
Volkmann, Lutz
ARS COMBINATORIA, 2011, 99 : 55 - 64
[44] Neighborhood conditions for graphs and digraphs to be maximally edge-connected
Hellwig, Angelika
Volkmann, Lutz
AUSTRALASIAN JOURNAL OF COMBINATORICS, 2005, 33 : 265 - 277
[45] Degree conditions for graphs to be maximally k-restricted edge connected and super k-restricted edge connected
Wang, Shiying
Zhao, Nana
DISCRETE APPLIED MATHEMATICS, 2015, 184 : 258 - 263
[46] Decomposing highly edge-connected graphs into paths of any given length
Botler, F.
Mota, G. O.
Oshiro, M. T. I.
Wakabayashi, Y.
JOURNAL OF COMBINATORIAL THEORY SERIES B, 2017, 122 : 508 - 542
[47] Super-edge-connected and Optimally Super-edge-connected Bi-Cayley graphs
Liu, Fengxia
Meng, Jixiang
ARS COMBINATORIA, 2010, 97A : 3 - 13
[48] Degree sequence conditions for maximally edge-connected oriented graphs
Volkmann, Lutz
APPLIED MATHEMATICS LETTERS, 2006, 19 (11) : 1255 - 1260
[49] Degree sequence conditions for maximally edge-connected graphs and digraphs
Dankelmann, P
Volkmann, L
JOURNAL OF GRAPH THEORY, 1997, 26 (01) : 27 - 34
[50] On m-restricted edge connectivity of undirected generalized De Bruijn graphs
Ou, Jianping
Li, Jiqing
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2013, 90 (11) : 2259 - 2264

← 1 2 3 4 5 →