Some years ago, the harmonic polynomial was introduced to study the harmonic topological
index. Here, using this polynomial, we obtain several properties of the harmonic index of …

We introduce the differential polynomial of a graph. The differential polynomial of a graph G
of order n is the polynomial B (G; x):= ∑ _ k=-n^ ∂ (G) B_k (G) x^ n+ k B (G; x):=∑ k …

The alliance polynomial of a graph G with order n and maximum degree Δ is the polynomial
A (G; x)=∑ k=− Δ Δ A k (G) x n+ k, where A k (G) is the number of exact defensive k-alliances …

Sea G=(V (G), E (G)) una gráfica simple, en el que V (G) y E (G) son sus conjuntos de
vértices y aristas respectivamente. Si S⊆ V (G), sea B (S) el conjunto de vértices con-tenido …

We introduce a new bivariate polynomial which we call the defensive alliance polynomial
and denote it by da (G; x, y). It is a generalization of the alliance polynomial [Carballosa et …

This chapter describes alliance polynomial of a graph with special attention to its
distinguishable power. The main contribution of this chapter is to prove that several well …