ABSTRACT. Suppose G is a graph, A(G) its adjacency matrix and f(G, x)=x^n+a_(n-1)x^(n-1)+... is the characteristic polynomial of G. The matching polynomial of G is defined as M(G, x) = x^n-m(G,1)x^(n-2) + ... where m(G,k) is the number of k-matchings in G. In this paper, we determine the relationship between 2k-th coefficient of characteristic polynomial, a_(2k), and k-th coefficient of matchin...

<p style='text-indent:20px;'>We continue our investigation of the parameter space families polynomial skew products. Assuming that base has a Julia set not totally disconnected and is neither Chebyshev nor power map, we prove that, near any bifurcation parameter, one can find parameters where <inline-formula><tex-math id="M1">\begin{document}$ k $\end{document}</tex-math&gt...

Abstract Let D be a finite-dimensional division algebra over its center and R = [ t ; ? , ? ] skew polynomial ring. Under certain assumptions on the ring of central quotients ( ) { f / g | ? ], C ])} is simple with reduced norm N . We calculate for some polynomials investigate when how reducibility reflects