Distance irredundance and connected domination numbers of a graph

Jun Ming Xu, Fang Tian, Jia Huang

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Let k be a positive integer and G be a connected graph. This paper considers the relations among four graph theoretical parameters: the k-domination number γk (G), the connected k-domination number γkc (G); the k-independent domination number γki (G) and the k-irredundance number irk (G). The authors prove that if an irk-set X is a k-independent set of G, then irk (G) = γk (G) = γki (G), and that for k ≥ 2, γkc (G) = 1 if irk (G) = 1, γkc (G) ≤ max { (2 k + 1) irk (G) - 2 k, frac(5, 2) irk (G) k - frac(7, 2) k + 2 } if irk (G) is odd, and γkc (G) ≤ frac(5, 2) irk (G) k - 3 k + 2 if irk (G) is even, which generalize some known results.

Original languageEnglish (US)
Pages (from-to)2943-2953
Number of pages11
JournalDiscrete Mathematics
Volume306
Issue number22
DOIs
StatePublished - Nov 28 2006

Fingerprint

Irredundance
Domination number
Independent Domination number
Graph in graph theory
Independent Set
Connected graph
Odd
Generalise
Integer

Keywords

  • Connected k-domination number
  • k-Domination number
  • k-Independent domination number
  • k-Independent set
  • k-Irredundance number

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

Cite this

Distance irredundance and connected domination numbers of a graph. / Xu, Jun Ming; Tian, Fang; Huang, Jia.

In: Discrete Mathematics, Vol. 306, No. 22, 28.11.2006, p. 2943-2953.

Research output: Contribution to journalArticle

Xu, Jun Ming ; Tian, Fang ; Huang, Jia. / Distance irredundance and connected domination numbers of a graph. In: Discrete Mathematics. 2006 ; Vol. 306, No. 22. pp. 2943-2953.
@article{914d0fc9e9384ef7a4f893d5f4226aa3,
title = "Distance irredundance and connected domination numbers of a graph",
abstract = "Let k be a positive integer and G be a connected graph. This paper considers the relations among four graph theoretical parameters: the k-domination number γk (G), the connected k-domination number γkc (G); the k-independent domination number γki (G) and the k-irredundance number irk (G). The authors prove that if an irk-set X is a k-independent set of G, then irk (G) = γk (G) = γki (G), and that for k ≥ 2, γkc (G) = 1 if irk (G) = 1, γkc (G) ≤ max { (2 k + 1) irk (G) - 2 k, frac(5, 2) irk (G) k - frac(7, 2) k + 2 } if irk (G) is odd, and γkc (G) ≤ frac(5, 2) irk (G) k - 3 k + 2 if irk (G) is even, which generalize some known results.",
keywords = "Connected k-domination number, k-Domination number, k-Independent domination number, k-Independent set, k-Irredundance number",
author = "Xu, {Jun Ming} and Fang Tian and Jia Huang",
year = "2006",
month = "11",
day = "28",
doi = "10.1016/j.disc.2006.03.075",
language = "English (US)",
volume = "306",
pages = "2943--2953",
journal = "Discrete Mathematics",
issn = "0012-365X",
publisher = "Elsevier",
number = "22",

}

TY - JOUR

T1 - Distance irredundance and connected domination numbers of a graph

AU - Xu, Jun Ming

AU - Tian, Fang

AU - Huang, Jia

PY - 2006/11/28

Y1 - 2006/11/28

N2 - Let k be a positive integer and G be a connected graph. This paper considers the relations among four graph theoretical parameters: the k-domination number γk (G), the connected k-domination number γkc (G); the k-independent domination number γki (G) and the k-irredundance number irk (G). The authors prove that if an irk-set X is a k-independent set of G, then irk (G) = γk (G) = γki (G), and that for k ≥ 2, γkc (G) = 1 if irk (G) = 1, γkc (G) ≤ max { (2 k + 1) irk (G) - 2 k, frac(5, 2) irk (G) k - frac(7, 2) k + 2 } if irk (G) is odd, and γkc (G) ≤ frac(5, 2) irk (G) k - 3 k + 2 if irk (G) is even, which generalize some known results.

AB - Let k be a positive integer and G be a connected graph. This paper considers the relations among four graph theoretical parameters: the k-domination number γk (G), the connected k-domination number γkc (G); the k-independent domination number γki (G) and the k-irredundance number irk (G). The authors prove that if an irk-set X is a k-independent set of G, then irk (G) = γk (G) = γki (G), and that for k ≥ 2, γkc (G) = 1 if irk (G) = 1, γkc (G) ≤ max { (2 k + 1) irk (G) - 2 k, frac(5, 2) irk (G) k - frac(7, 2) k + 2 } if irk (G) is odd, and γkc (G) ≤ frac(5, 2) irk (G) k - 3 k + 2 if irk (G) is even, which generalize some known results.

KW - Connected k-domination number

KW - k-Domination number

KW - k-Independent domination number

KW - k-Independent set

KW - k-Irredundance number

UR - http://www.scopus.com/inward/record.url?scp=33749233798&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33749233798&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2006.03.075

DO - 10.1016/j.disc.2006.03.075

M3 - Article

AN - SCOPUS:33749233798

VL - 306

SP - 2943

EP - 2953

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 22

ER -