$$F_{3}$$ -domination problem of graphs

Chan-Wei Chang (), David Kuo (), Sheng-Chyang Liaw () and Jing-Ho Yan ()
Additional contact information
Chan-Wei Chang: National Dong Hwa University
David Kuo: National Dong Hwa University
Sheng-Chyang Liaw: National Central University
Jing-Ho Yan: Aletheia University

Journal of Combinatorial Optimization, 2014, vol. 28, issue 2, No 6, 400-413

Abstract: Abstract Given a graph $$G$$ and a set $$S\subseteq V(G),$$ a vertex $$v$$ is said to be $$F_{3}$$ -dominated by a vertex $$w$$ in $$S$$ if either $$v=w,$$ or $$v\notin S$$ and there exists a vertex $$u$$ in $$V(G)-S$$ such that $$P:wuv$$ is a path in $$G$$ . A set $$S\subseteq V(G)$$ is an $$F_{3}$$ -dominating set of $$G$$ if every vertex $$v$$ is $$F_{3}$$ -dominated by a vertex $$w$$ in $$S.$$ The $$F_{3}$$ -domination number of $$G$$ , denoted by $$\gamma _{F_{3}}(G)$$ , is the minimum cardinality of an $$F_{3}$$ -dominating set of $$G$$ . In this paper, we study the $$F_{3}$$ -domination of Cartesian product of graphs, and give formulas to compute the $$F_{3}$$ -domination number of $$P_{m}\times P_{n}$$ and $$P_{m}\times C_{n}$$ for special $$m,n.$$

Keywords: Domination; $$F_{3}$$ -domination; Cartesian product; Path; Cycle (search for similar items in EconPapers)
Date: 2014
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10878-012-9563-y Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jcomop:v:28:y:2014:i:2:d:10.1007_s10878-012-9563-y

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10878

DOI: 10.1007/s10878-012-9563-y

Access Statistics for this article

Journal of Combinatorial Optimization is currently edited by Thai, My T.

More articles in Journal of Combinatorial Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().