Strong Non Split Block Domination in Graphs

Abstract

For any graph G=( V,E ), the block graph B(G) is a graph whose set of vertices is the union of the set of blocks of G in which two vertices are adjacent if and only if the corresponding blocks of G are adjacent. A dominating set D of a graph B(G) is a strong non split block dominating set if the induced sub graph ?V[B(G) ]-D? is complete. The strong non split block domination number? ??_(snsb ) (G) of G is the minimum cardinality of strong non split block dominating set of G. In this paper, we study graph theoretic properties of ? ??_(snsb ) (G) and many bounds were obtain in terms of elements of G and its relationship with other domination parameters were found.
DOI: 10.17762/ijritcc2321-8169.1507126