a neighborhood condition and characteristic polynomials of somegraphs

A simple graph is called n-bounded if for every two nonadjacent vertices x; y, there exists a vertex zsuch that n(x) [ n(y) ⊆ n(z) [ fzg. it is shown that any regular graph is complete r-partite with partsof the same size, where r is the number of the connected components of g and then its characteristicpolynomial is computed. also, the structure and the adjacency spectrum of n-bounded bipartite graphsare studied. finally the number of nonzero eigenvalues of an n-bounded bipartite graph is determined.