Polytopality and Cartesian products of graphs

We study the question of polytopality of graphs: when is a given graph the graph of a polytope? We first review the known necessary conditions for a graph to be polytopal, and we provide several families of graphs which satisfy all these conditions, but which nonetheless are not graphs of polytopes. Our main contribution concerns the polytopality of Cartesian products of non-polytopal graphs. On the one hand, we show that products of simple polytopes are the only simple polytopes whose graph is a product. On the other hand, we provide a general method to construct (non-simple) polytopal products whose factors are not polytopal.Comment: 21 pages, 10 figure

Controlled release from zein matrices: Interplay of drug hydrophobicity and pH

Purpose: In earlier studies, the corn protein zein is found to be suitable as a sustained release agent, yet the range of drugs for which zein has been studied remains small. Here, zein is used as a sole excipient for drugs differing in hydrophobicity and isoelectric point: indomethacin, paracetamol and ranitidine. Methods: Caplets were prepared by hot-melt extrusion (HME) and injection moulding (IM). Each of the three model drugs were tested on two drug loadings in various dissolution media. The physical state of the drug, microstructure and hydration behaviour were investigated to build up understanding for the release behaviour from zein based matrix for drug delivery. Results: Drug crystallinity of the caplets increases with drug hydrophobicity. For ranitidine and indomethacin, swelling rates, swelling capacity and release rates were pH dependent as a consequence of the presence of charged groups on the drug molecules. Both hydration rates and release rates could be approached by existing models. Conclusion: Both the drug state as pH dependant electrostatic interactions are hypothesised to influence release kinetics. Both factors can potentially be used factors influencing release kinetics release, thereby broadening the horizon for zein as a tuneable release agent