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 ...

Finally, we conclude by discussing the domination polynomials of a related family of graphs, the 𝑛-book graphs 𝐵𝑛, formed by joining 𝑛 copies of the cycle graph 𝐶₄ with a common edge. The journal ...

How can the tiniest particles and the vast structure of the universe be explained using the same kind of mathematics? This puzzle is the focus of recent research by mathematicians Claudia Fevola ...

Jason I. Brown and Julia Tufts, On the Roots of Domination Polynomials, Graphs and Combinatorics, accepted for publication. Jason I. Brown, Karl Dilcher and Dante Manna, On a Sequence of Sparse ...

By exploring positive geometry, mathematicians are revealing hidden shapes that may unify particle physics and cosmology, offering new ways to understand both collisions in accelerators and the ...