Note on the domination number of graphs with forbidden cycles of lengths not divisible by 3

被引：0

作者：

Khoeilar, R. ^{[1
]}

Karami, H. ^{[1
]}

Chellali, M. ^{[2
]}

Sheikholeslami, S. M. ^{[1
]}

机构：

[1] Azarbaijan Shahid Madani Univ, Dept Math, Tabriz, Iran

[2] Univ Blida, Dept Math, LAMDA RO Lab, BP 270, Blida, Algeria

来源：

AUSTRALASIAN JOURNAL OF COMBINATORICS | 2022年 / 83卷

关键词：

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this note, we prove that the domination number of a graph of order n and minimum degree at least 2 that does not contain cycles of length 3r + 2, where 1 <= r <= k, and cycles of length 3r + 1 for 1 <= r <= 2k + 2, is at most k+2/3k +5n. This improves some previous results.

引用

页码：101 / 108

页数：8

共 50 条

[1] Split domination number of divisible dominating graphs
Amutha, S.
Prabha, K. Suriya
Anbazhagan, N.
Shanthi, P.
JOURNAL OF DISCRETE MATHEMATICAL SCIENCES & CRYPTOGRAPHY, 2021, 24 (04): : 997 - 1006
[2] A note on the independent domination number in graphs
Rad, Nader Jafari
Volkmann, Lutz
DISCRETE APPLIED MATHEMATICS, 2013, 161 (18) : 3087 - 3089
[3] A note on the independent domination number versus the domination number in bipartite graphs
Shaohui Wang
Bing Wei
Czechoslovak Mathematical Journal, 2017, 67 : 533 - 536
[4] A note on the Italian domination number and double Roman domination number in graphs
Hajibaba, Maryam
Rad, Nader Jafari
Journal of Combinatorial Mathematics and Combinatorial Computing, 2019, 109 : 169 - 183
[5] A note on the independent domination number versus the domination number in bipartite graphs
Wang, Shaohui
Wei, Bing
CZECHOSLOVAK MATHEMATICAL JOURNAL, 2017, 67 (02) : 533 - 536
[6] Maximising the number of cycles in graphs with forbidden subgraphs
Morrison, Natasha
Roberts, Alexander
Scott, Alex
JOURNAL OF COMBINATORIAL THEORY SERIES B, 2021, 147 : 201 - 237
[7] Domination Number of Graphs Without Small Cycles
Chen, Xue-gang
Sohn, Moo Young
GRAPHS AND COMBINATORICS, 2011, 27 (06) : 821 - 830
[8] Domination Number of Graphs Without Small Cycles
Xue-gang Chen
Moo Young Sohn
Graphs and Combinatorics, 2011, 27 : 821 - 830
[9] A Note on the Double Roman Domination Number of Graphs
Chen, Xue-gang
CZECHOSLOVAK MATHEMATICAL JOURNAL, 2020, 70 (01) : 205 - 212
[10] A note on weakly connected domination number in graphs
Chen, Xue-gang
Shiu, Wai Chee
ARS COMBINATORIA, 2010, 97 : 193 - 201

← 1 2 3 4 5 →