Some Parameters on Neighborhood Number of A Graph

A set S⊆V is a neighborhood set of G , if G=⋃v∈S〈N[v]〉, where 〈N[v]〉 is the sub graph of G induced by v and all vertices adjacent to v . The neighborhood number η(G) of G is the minimum cardinality of a neighborhood set of G. In this paper, we extended the concept of neighborhood number and its relationship with other related parameters are explored

The Dual Neighborhood Number of a Graph

A set S ⊆ V (G) is a neighborhood set of a graph G = (V,E), if G = v∈SN[v]�, where N[v]� is the sub graph of a graph G induced by v and all vertices adjacent to v. The dual neighborhood number η+2(G) = Min. {|S1|+ |S2| : S1, S2 are two disjoint neighborhood set of G}. In this paper, we extended the concept of neighborhood number to dual neighborhood number and its relationship with other neighborhood related parameters are explored.