Abstract: A
set SÍVis
a neighborhood set of G, if where
áN[v]ñis
the subgraph of G
induced by v
and all vertices adjacent to v.
The neighborhood number h(G)of
G is
the minimum cardinality of a neighborhood set
of G. A neighborhood set SÍVis
a paired-neighborhood set if the induced
subgraph áSñ
contains at least one perfect matching. The
paired-neighborhood number of G, denoted by hPair(G),is
the smallest cardinality of a
paired-neighborhood set of G.
In this paper, we determine a best possible
upper and lower bound for hPair(G),and
its exact values for some particular classes
of graphs are found. Also its relationship
with other parameters is investigated.
