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 Hirsch conjecture states that the combinatorial diameter of every convex d-polytope with n facets is bounded by n-d. Hirsch Conjecture (1957): Let P be a convex d-polytope with n facets. Then the ...

We study the asymptotic behavior of the asymptotic translation lengths on the curve complexes of pseudo-Anosov monodromies in a fibered cone of a fibered hyperbolic 3-manifold M with b1(M) ≥ 2. For a ...

The Hosoya polynomial H(G, λ) of a graph G has the property that its first derivative at λ = 1 is equal to the Wiener index. Sometime ago two distance-based graph invariants were studied - the Schultz ...

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 ...