1. Preliminaries The Kirchhoff index was introduced in chemistry as a better alternative to other parameters used for discriminating among different molecules with similar shapes and structures; see… (More)

In this paper we present a procedure for the numerical estimation of the Fekete points of a wide variety of compact sets in IR. We understand the problem of the Fekete points in terms of the… (More)

We aim here at introducing a new point of view of the Laplacian of a graph, Γ. With this purpose in mind, we consider L as a kernel on the finite space V (Γ), in the context of the Potential Theory.… (More)

We show here that the Kirchhoff index of a network is the average of the Wiener capacities of its vertices. Moreover, we obtain a closed-form formula for the effective resistance between any pair of… (More)

Here we study the computational complexity of the Fekete point problem. Namely, we give an exhaustive description of the main properties of an algorithm for the search of the logarithmic Fekete… (More)

We consider the Laplacian of a finite network as a kernel on the vertex set. The properties of this kernel allow us to assign to every proper set an equilibrium measure and a capacity. So, we can… (More)

In this work we define a class of non self–adjoint boundary value problems on finite networks associated with Schrödinger operators. The novelty lies on the fact that on a part of the boundary no… (More)

Our aim is to characterize those matrices that are the response matrix of a semi–positive definite Schrödinger operator on a circular planar network. Our findings generalize the known results and… (More)