An independent dominating set in the complement of a minimum dominating set of a tree

Michael A. Henning; Christian Löwenstein; Dieter Rautenbach

doi:10.1016/j.aml.2009.08.008

An independent dominating set in the complement of a minimum dominating set of a tree

Michael A. Henning, Christian Löwenstein, Dieter Rautenbach

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

We prove that for every tree T of order at least 2 and every minimum dominating set D of T which contains at most one endvertex of T, there is an independent dominating set I of T which is disjoint from D. This confirms a recent conjecture of Johnson, Prier, and Walsh.

Original language	English
Pages (from-to)	79-81
Number of pages	3
Journal	Applied Mathematics Letters
Volume	23
Issue number	1
DOIs	https://doi.org/10.1016/j.aml.2009.08.008
Publication status	Published - Jan 2010
Externally published	Yes

Keywords

Domination
Independence
Inverse domination

ASJC Scopus subject areas

Applied Mathematics

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10.1016/j.aml.2009.08.008

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title = "An independent dominating set in the complement of a minimum dominating set of a tree",

abstract = "We prove that for every tree T of order at least 2 and every minimum dominating set D of T which contains at most one endvertex of T, there is an independent dominating set I of T which is disjoint from D. This confirms a recent conjecture of Johnson, Prier, and Walsh.",

keywords = "Domination, Independence, Inverse domination",

author = "Henning, {Michael A.} and Christian L{\"o}wenstein and Dieter Rautenbach",

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AU - Henning, Michael A.

AU - Löwenstein, Christian

AU - Rautenbach, Dieter

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Y1 - 2010/1

N2 - We prove that for every tree T of order at least 2 and every minimum dominating set D of T which contains at most one endvertex of T, there is an independent dominating set I of T which is disjoint from D. This confirms a recent conjecture of Johnson, Prier, and Walsh.

AB - We prove that for every tree T of order at least 2 and every minimum dominating set D of T which contains at most one endvertex of T, there is an independent dominating set I of T which is disjoint from D. This confirms a recent conjecture of Johnson, Prier, and Walsh.

KW - Domination

KW - Independence

KW - Inverse domination

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U2 - 10.1016/j.aml.2009.08.008

DO - 10.1016/j.aml.2009.08.008

M3 - Article

AN - SCOPUS:70350618307

SN - 0893-9659

VL - 23

SP - 79

EP - 81

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

IS - 1

ER -

An independent dominating set in the complement of a minimum dominating set of a tree

Abstract

Keywords

ASJC Scopus subject areas

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