Weak Domination in Block Graphs

M. H. Muddebihal; Geetadevi Baburao

Research Article

Weak Domination in Block Graphs

by M. H. Muddebihal, Geetadevi Baburao

International Journal of Applied Information Systems

Foundation of Computer Science (FCS), NY, USA

Volume 12 - Issue 27

Published: February 2020

Authors: M. H. Muddebihal, Geetadevi Baburao

10.5120/ijais2020451844

PDF

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 },
                        year    = { 2020 },
                        volume  = { 12 },
                        number  = { 27 },
                        pages   = { 15-20 },
                        doi     = { 10.5120/ijais2020451844 },
                        publisher = { Foundation of Computer Science (FCS), NY, USA }
                        }

                        %0 Journal Article
                        %D 2020
                        %A M. H. Muddebihal
                        %A Geetadevi Baburao
                        %T Weak Domination in Block Graphs%T 
                        %J International Journal of Applied Information Systems
                        %V 12
                        %N 27
                        %P 15-20
                        %R 10.5120/ijais2020451844
                        %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

No index terms available.

Keywords

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