Irreducibility of a Polynomial Shifted by a Power of Another Polynomial

extensions of some polynomial inequalities to the polar derivative

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Testing polynomial irreducibility without GCDs

We determine classes of degrees where testing irreducibility for univariate polynomials over finite fields can be done without any GCD computation. This work was partly funded by the INRIA Associate Team “Algorithms, Numbers, Computers” (http://www.loria.fr/~zimmerma/anc.html). Key-words: finite fields, irreducible polynomial, GCD ∗ ANU, Canberra, [email protected] Test d’irréductibilité de polynôme...

On the polar derivative of a polynomial

For a polynomial p(z) of degree n, having all zeros in |z|< k, k< 1, Dewan et al [K. K. Dewan, N. Singh and A. Mir, Extension of some polynomial inequalities to the polar derivative, J. Math. Anal. Appl. 352 (2009) 807-815] obtained inequality between the polar derivative of p(z) and maximum modulus of p(z). In this paper we improve and extend the above inequality. Our result generalizes certai...

On Szeged Polynomial of a Graph

On the Roots of Hosoya Polynomial of a Graph

Let G = (V, E) be a simple graph. Hosoya polynomial of G is d(u,v) H(G, x) = {u,v}V(G)x , where, d(u ,v) denotes the distance between vertices u and v. As is the case with other graph polynomials, such as chromatic, independence and domination polynomial, it is natural to study the roots of Hosoya polynomial of a graph. In this paper we study the roots of Hosoya polynomials of some specific g...