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 ...

Let 𝑛 be any positive integer and 𝐹𝑛 be the Friendship graph with 2𝑛 + 1 vertices and 3𝑛 edges, formed by the join of 𝐾₁ with 𝑛𝐾₂. We study the domination polynomials of this family of graphs, ...