Abstract: Let be
a graph. A set A of vertices in a graph G is
a neighbourhood set of G, ifwhereis
the subgraph of G induced by v
and all vertices adjacent to v.A neighbourhood set A is
said to be a block neighbourhood set if is a block in G.
The block neighbourhood number of
G is the minimum cardinality of a
block neighbourhood set of G. In this
paper, bounds for and
its exact values for some particular classes of graphs are found. Also, a
Nordhaus-Gaddum type result is established for
