• STRONG NONSPLIT LINE SET DOMINATING NUMBER OF GRAPH

Abstract

I. H. Nagaraja Rao & B. Vijayalakmi introduced the concept of Line set domination number of a Graph and derived results parallel to those of E.Sampathkumar and L. Pushpalatha. Let G be a graph. A set F⊆E(G) is a line set dominating set (LSD-set) of G. if for each set L ⊆ E –F,  there exists an edge e in F such that the subgraph                   {< L∪ {e}>} induced by L∪ {e} is connected.  (ϑʹ_l (G)). V.R. Kulli and B.Janakiram introduced the concept of non-split domination number of a graph and derived results parallel. A dominating set F of a graph of G is a strong nonsplit dominating set if the induced subgraph (E-F) is complete.  The Stong nonsplit domination number (𝜸sns(G)) of G is the minimum cardinality of strong nonsplit dominating set. Combining the two concepts Strong nonsplit line set dominating set is introduced as follows, A line set dominating set L⊆E(G)  of a graph G=(V,E) is said to be a Strong nonsplit line set dominating set. if the induced subgraph <E-L> is complete. A Strong nonsplit line set dominating number ϑʹsnsl (G) of G  is the minimum cardinality of a Strong nonsplit line set dominating set. In this paper we analyse the dominating parameters corresponding to Strong nonsplit line set dominating set and obtain the some bounds and some exact value for ((ϑʹ snsl (G).