Graph polynomials serve as robust algebraic encodings of the intricate combinatorial properties inherent to graphs. At the heart of this discipline lies the Tutte polynomial, an invariant that not ...

We add a fixed number of vertices of degree 1 to each vertex from one part of a bipartite graph. We study characteristic, matching and some related polynomials for graphs obtained in this way.

We give explicit representations of the coefficients of p-valent functions which are polynomials of univalent functions of the class S. With their help we prove the Goodman conjecture in the special ...