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 ...

The second path matrix S(G) collects all the second paths in the graph G. Its characteristic polynomial shows some regularity in several particular graphs, such as paths, cycles, stars and complete ...

The quantum Bruhat graph, which is an extension of the graph formed by covering relations in the Bruhat order, is naturally related to the quantum cohomology ring of G/B. We enhance a result of Fulton ...

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 ...