The paper proves by means of the state space theory the theorem in which the characteristic polynomial of the determinate feedback connection of two controllable and observable dynamical systems is stated. The characteristic polynomial is expressed by the use of the transfer function matrices of each dynamical system.

We show that a number of graph invariants are, even combined, insufficient to distinguish between nonisomorphic trees or general graphs. Among these are: the spectrum of eigenvalues (equivalently, the characteristic polynomial), the number of independent sets of all sizes or the number of connected subgraphs of all sizes. We therefore extend the classical theorem of Schwenk that almost every tr...

Abstract. The complexity of a graph can be obtained as a derivative of a variation of the zeta function [J. Combin. Theory Ser. B, 74 (1998), pp. 408–410] or a partial derivative of its generalized characteristic polynomial evaluated at a point [arXiv:0704.1431[math.CO]]. A similar result for the weighted complexity of weighted graphs was found using a determinant function [J. Combin. Theory Se...