Point Set and Strong Point Set Domination in Graphs 1 Minimum spsd sets

Point set domination was introduced by E. Sampathkumar et al in the paper titled ‘POINT SET DOMINATION NUMBER OF A GRAPH’. A subset D of V(G) of a connected graph G is a point set dominating set (psd - set) of G if for every T ⊆ V - D there exists d ∈ D such that the subgraph < T ⨆ {d} > induced by T ⨆ {d} is connected. The point set domination number γp(G) is the cardinality of a minimum psd set. In this paper we define the following: et D ⊆ V(G) is said to be a strong point set dominating set (spsd set) of G if for every T ⊆ V - D there exists a vertex d ∈ D such that the subgraph < T ⊆{d} > induced by T ⨆ {d} is connected and deg d ≥ deg t for all t ∈ T. e cardinality of minimum spsd set is called the strong point set domination number and is denoted by γsp (G) f A ⊆ V then N(A) = the set of all neighbours of vertices in A and N[A] = A⨆N(A). r a complete block B, B+Δ is obtained by the adjunction of a vertex of deg Δ at each vertex of the block. = max {∣B∣ − γsp (B)} where BG denote the set of all blocks of G.