Simultaneous graph parameters: Factor domination and factor total domination

Peter Dankelmann; Michael A. Henning; Wayne Goddard; Renu Laskar

doi:10.1016/j.disc.2006.04.017

Simultaneous graph parameters: Factor domination and factor total domination

Peter Dankelmann, Michael A. Henning, Wayne Goddard, Renu Laskar

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

4 Citations (Scopus)

Abstract

Let F₁, F₂, ..., F_k be graphs with the same vertex set V. A subset S ⊆ V is a factor dominating set if in every F_i every vertex not in S is adjacent to a vertex in S, and a factor total dominating set if in every F_i every vertex in V is adjacent to a vertex in S. The cardinality of a smallest such set is the factor (total) domination number. In this note, we investigate bounds on the factor (total) domination number. These bounds exploit results on colorings of graphs and transversals of hypergraphs.

Original language	English
Pages (from-to)	2229-2233
Number of pages	5
Journal	Discrete Mathematics
Volume	306
Issue number	18
DOIs	https://doi.org/10.1016/j.disc.2006.04.017
Publication status	Published - 28 Sept 2006
Externally published	Yes

Keywords

Bounds
Cycles
Factors
Total domination

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2006.04.017

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AU - Laskar, Renu

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N2 - Let F1, F2, ..., Fk be graphs with the same vertex set V. A subset S ⊆ V is a factor dominating set if in every Fi every vertex not in S is adjacent to a vertex in S, and a factor total dominating set if in every Fi every vertex in V is adjacent to a vertex in S. The cardinality of a smallest such set is the factor (total) domination number. In this note, we investigate bounds on the factor (total) domination number. These bounds exploit results on colorings of graphs and transversals of hypergraphs.

AB - Let F1, F2, ..., Fk be graphs with the same vertex set V. A subset S ⊆ V is a factor dominating set if in every Fi every vertex not in S is adjacent to a vertex in S, and a factor total dominating set if in every Fi every vertex in V is adjacent to a vertex in S. The cardinality of a smallest such set is the factor (total) domination number. In this note, we investigate bounds on the factor (total) domination number. These bounds exploit results on colorings of graphs and transversals of hypergraphs.

KW - Bounds

KW - Cycles

KW - Factors

KW - Total domination

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Simultaneous graph parameters: Factor domination and factor total domination

Abstract

Keywords

ASJC Scopus subject areas

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