Inverse eigenvalue problem for constructing a kind of acyclic matrices with two eigenpairs

summary:We investigate an inverse eigenvalue problem for constructing a special kind of acyclic matrices. The problem involves the reconstruction of the matrices whose graph is an $m$-centipede. This is done by using the $(2m-1)$st and $(2m)$th eigenpairs of their leading principal submatrices. To solve this problem, the recurrence relations between leading principal submatrices are used