Roberto Cruz

Wiener index of Eulerian graphs

The Wiener index of a connected graph G is the sum of distances between all pairs of vertices of G . We characterize Eulerian graphs (with a fixed number of vertices) with smallest and greatest Wiener indices.

Parallelizing a heuristic for the Maximum Clique Problem on GPUs and clusters of workstations

A heuristic for the Maximum Clique Problem was parallelized on a Graphical Processing Unit and a cluster of workstations. The heuristic is based on a formulation based on neural networks. Performance results are reported.

Parallelizing an algorithm to find the maximal clique on interval graphs on graphical processing units

An algorithm to find the maximal clique on an interval graphs was parallelized on Graphical Processing Units. The algorithm was implemented using CUDA and the Thrust library. Performance results are reported.

Topological indices of Kragujevac trees

We find the extremal values of the energy, the Wiener index and several vertex-degree-based topological indices over the set of Kragujevac trees with the central vertex of fixed degree.

Vertex-degree-based topological indices over starlike trees

Given a graph G with n vertices, a vertex-degree-based topological index is defined from a set of real numbers { ? i j } as T I ( G ) = ? m i j ( G ) ? i j , where m i j ( G ) is the number of edges between vertices of degree i and degree j , and the sum runs over all 1 ? i ? j ? n - 1 . We find conditions on the numbers { ? i j } which are easy to verify, under which the extremal values of T I over the set of starlike trees can be calculated. As an application we find the extremal values of many well-known vertex-degree-based topological indices over ? n .

Parallelizing an algorithm to decide if a bipartite graph is shellable

An algorithm to decide if a bipartite graph is shellable was parallelized using pthreads. Performance results are reported.

Variable selection by recurrent neural networks. Application in structure activity relationship study of cephalosporins

Two methods for variable selection which are efficiently implemented by Hopfield-like Neural networks are described. Qualitative SAR models using the selected variables by both neural networks variable selection methods are built. The biological activity against Staphylococcus aureus of cephalosporins was used as dependent variable. The final correlation between observed and predicted activity values are good, indicating that the informative weight of the favored variables is high, providing a sound basis to select a good variable set of in qualitative structure-activity relationships (SAR) modeling.