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 ...