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Weak Domination in Block Graphs

M. H. Muddebihal, Geetadevi Baburao in Applied Mathematics

International Journal of Applied Information Systems
Year of Publication: 2020
Publisher: Foundation of Computer Science (FCS), NY, USA
Series: Volume 12 Number 27
Authors:M. H. Muddebihal, Geetadevi Baburao
10.5120/ijais2020451844
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  1. M H Muddebihal and Geetadevi Baburao. Weak Domination in Block Graphs. International Journal of Applied Information Systems 12(27):15-20, February 2020. URL, DOI BibTeX

    @article{10.5120/ijais2020451844,
	author = "M. H. Muddebihal and Geetadevi Baburao",
	title = "Weak Domination in Block Graphs",
	journal = "International Journal of Applied Information Systems",
	issue_date = "February 2020",
	volume = 12,
	number = 27,
	month = "February",
	year = 2020,
	issn = "2249-0868",
	pages = "15-20",
	url = "http://www.ijais.org/archives/volume12/number27/1078-2020451844",
	doi = "10.5120/ijais2020451844",
	publisher = "Foundation of Computer Science (FCS), NY, USA",
	address = "New York, USA"
}

Abstract

For any graph G=(V,E), the block graph B(G) is a graph whose set of vertices is the union of set of blocks of G in which two vertices are adjacent if and only if the corresponding blocks of G are adjacent. For any two adjacent vertices u and v we say that v weakly dominates u if deg(v)=deg(u). A dominating set D of a graph B(G) is a weak block dominating set of B(G), if every vertex in V[B(G) ]-D is weakly dominated by at least one vertex in D. A weak domination number of a block graph B(G) is the minimum cardinality of a weak dominating set of B(G). In this paper, we study a graph theoretic properties of γWB (G) and many bounds were obtained in terms of elements of G and the relationship with other domination parameters were found.

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Keywords

Dominating set; Strong split domination; Weak domination; Perfect domination; Weak block domination