Alzheimer’s Disease (AD) is an incurable neurodegenerative disorder which mainly affects older adults. An early diagnosis essential because medical treatments can slow down the progression of disease only if provided during first stage, called Mild Cognitive Impairment (MCI). Starting from study electroencephalografic signals, brain functional connectivity analyses be performed with support gra...

The Randić index of a graph G is defined as R(G) = ∑ u∼v (d(u)d(v))− 2 , where d(u) is the degree of vertex u, and the summation goes over all pairs of adjacent vertices u, v. A conjecture of R(G) for connected graph with n vertices is as follows: R(G)−D √2− n+1 2 and R(G) D 1 2 + √ 2−1 n−1 , where D is the diameter of G. In this paper, we prove that this conjecture is true for unicyclic graphs.

Let G be a collection of graphs with n vertices. We present a simple description of [G]χ = {H ∈ G : χ(H) = χ(G)} where χ denotes the Randić index. We associate to G a Q-linear map ρ : Qm → Qk (for some integers k, m depending on G) such that the kernel of ρ contains the necessary information to describe [G]χ in terms of linear equations. These results provide precise tools for analyzing the beh...

We develop the idea that the use of ad hoc molecular descriptors in QSAR/QSPR studies is not an optimal solution. Instead, we propose to optimize these descriptors for the specific properties under study. In the case of topological indices (TIs) we propose the use of the generalized topological indices (GTIs), which account for several of the classical TIs in one single graph invariant. GTIs re...