We solve the design spectrum problem for all theta graphs with 10, 11, 12, 13, 14 and 15 edges.

the crossing number of a graph  is the minimum number of edge crossings over all possible drawings of  in a plane. the crossing number is an important measure of the non-planarity of a graph, with applications in discrete and computational geometry and vlsi circuit design. in this paper we introduce vertex centered crossing number and study the same for maximal planar graph.

Abstract Deep learning methods applied to chemistry can be used accelerate the discovery of new molecules. This work introduces GraphINVENT, a platform developed for graph-based molecular design using graph neural networks (GNNs). GraphINVENT uses tiered deep network architecture probabilistically generate molecules single bond at time. All models implemented in quickly learn build resembling t...

Abstract Rational drug design deals with computational methods to accelerate the development of new drugs. Among other tasks, it is necessary analyze huge databases small molecules. Since a direct relationship between structure these molecules and their effect (e.g., toxicity) can be assumed in many cases, wide set based on modeling as graphs attributes. Here, we discuss our results concerning ...