Weak Domination in Block Graphs
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