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Weak Domination in Block Graphs

by M. H. Muddebihal, Geetadevi Baburao
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International Journal of Applied Information Systems
Foundation of Computer Science (FCS), NY, USA
Volume 12 - Number 27
Year of Publication: 2020
Authors: M. H. Muddebihal, Geetadevi Baburao
10.5120/ijais2020451844

M. H. Muddebihal, Geetadevi Baburao . Weak Domination in Block Graphs. International Journal of Applied Information Systems. 12, 27 ( February 2020), 15-20. DOI=10.5120/ijais2020451844

@article{ 10.5120/ijais2020451844,
author = { M. H. Muddebihal, 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 },
numpages = {9},
url = { https://www.ijais.org/archives/volume12/number27/1078-2020451844/ },
doi = { 10.5120/ijais2020451844 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2023-07-05T19:10:09.783618+05:30
%A M. H. Muddebihal
%A Geetadevi Baburao
%T Weak Domination in Block Graphs
%J International Journal of Applied Information Systems
%@ 2249-0868
%V 12
%N 27
%P 15-20
%D 2020
%I Foundation of Computer Science (FCS), NY, 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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Index Terms

Computer Science
Information Sciences

Keywords

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

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