In this paper, we establish some upper bound estimates for the maximum modulus of the higher order derivative of a polynomial with RESTRICTED ZEROS on a circle of , , in terms of the maximum modulus of the same polynomial on the unit circle . These results generalize and sharpen some known results in this direction.

Please click on PDF to view the abstract.

We apply numerical radius and spectral radius estimates to the Frobenius companion matrices of monic POLYNOMIALS to derive new bounds for their ZEROS and give different proofs of some known bounds.

In this paper, we establish some Bernstein type inequalities for the complex polynomial. Our results constitute generalizations and re nements of some well-known polynomial inequalities.

Please click on PDF to view the abstract.

The matching polynomial of a graph has coefficients that give the number of matchings in the graph. In this paper, we determine all connected graphs on eight vertices whose matching POLYNOMIALS have only integer ZEROS. A graph is matching integral if the ZEROS of its matching polynomial are all integers. We show that there are exactly two matching integral graphs on eight vertices.