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 ...

Abstract. Let 𝐼(𝐺;𝑥) denote the independence polynomial of a graph 𝐺. In this paper we study the unimodality properties of 𝐼(𝐺;𝑥) for some composite graphs 𝐺. Given two graphs 𝐺₁ and 𝐺₂, let ...

A three-complex-parameter class of orthogonal Laurent polynomials on the unit circle associated with basic hypergeometric or q-hypergeometric functions is considered. To be precise, we consider the ...

Illustration of a set of real zeros of a graph polynomial (middle) and two Feynman diagrams. Credit: Max Planck Institute for Mathematics in the Sciences How can the behavior of elementary particles ...