Intern. J. Fuzzy Mathematical Archive

Abstract. A vertex v is a boundary vertex of u if d(u, w) ≤ d(u, v) for all w ∈ N(v). A vertex u have more than one boundary vertex at different distance levels. A vertex v is called a boundary neighbour of u if v is a nearest boundary of u. A set S ⊆V(G) is a bd – dominating set such that every vertex in V-S has at least one neighbour and at least one boundary neighbour in S. The cardinality of the minimum bd- dominating set is called the bd- domination number and is denoted by γbd(G).In this paper we present several bounds on the bd- domination number and exact values of particular graphs