Generalized inverse eigenvalue problem for matrices whose graph is a path

In this paper, we analyse a special generalized inverse eigenvalue problem Anx=λBnxAnx=λBnx for the pair (An,Bn)(An,Bn) of matrices each of whose graph is a path on n   vertices, by investigating the leading principal minors of the matrix An−λBnAn−λBn. From the given data consisting of BnBn, a matrix AkAk (k