Change of nullity of a graph under two operations

The nullity of a graph G is the multiplicity zero as an eigenvalue its adjacency matrix. An assignment weights to vertices graph, that satisfies sum condition over neighbors each vertex, and uses maximum number independent variables denoted by high weighting graph. This applicable tool used determine Two types graphs are defined, change their nullities studied, namely, G+ab constructed from adding new vertex ab which joint all both b G, G•ab obtained removing b.