We give a deterministic algorithm for triangulating a simple polygon in linear time. The basic strategy is to build a coarse approximation of a triangulation in a bottom-up phase and then use the information computed along the way to refine the triangulation in a top-down phase. The main tools used are the polygon-cutting theorem, which provides us with a balancing scheme, and the planar separator theorem, whose role is essential in the discovery of new diagonals. Only elementary data structures are required by the algorithm. In particular, no dynamic search trees, of our algorithm.

Triangulating a simple polygon in linear time

Book Review: Introduction to the Theory of Benzenoid Hydrocarbons . by Ivan Gutman and Sven J. Cyvin; Springer-Verlag, Berlin, 1989, pp ix + 152, price DM 148

Topological Indices and Their Applications to Circumcised Donut Benzenoid Systems, Kekulenes and Drugs

In this study we consider relatively new bond-additive Mostar indices that appear to provide quantitative measures of peripheral shapes of molecules. We have computed weighted Mostar, edge-Mostar and total-Mostar indices of graphene, [Formula: see text]-types of graphyne and graphdiyne, which are of considerable interest owing to their novel properties and thus find applications in a number of areas such as sensors, catalysis, chemisorption and nanomedicine. We have implemented the results to analyse the weighted Mostar indices and have obtained exact analytical expressions for the title molecules. We propose that Mostar indices together with frontier molecular orbitals, and HOMO-LUMO gaps can provide measures of chemical reactivity and analysis of peripheral molecular shapes.

Weighted Mostar indices as measures of molecular peripheral shapes with applications to graphene, graphyne and graphdiyne nanoribbons.

Quantitative structure-activity and structure-property relationships of complex polycyclic benzenoid networks require expressions for the topological properties of these networks Structure-based topological indices of these networks enable prediction of chemical properties and the bioactivities of these compounds through quantitative structure-activity and structure-property relationships methods We consider a number of infinite convex benzenoid networks that include polyacene, parallelogram, trapezium, triangular, bitrapezium, and circumcorone series benzenoid networks For all such networks, we compute analytical expressions for both vertex-degree and edge-based topological indices such as edge-Wiener, vertex-edge Wiener, vertex-Szeged, edge-Szeged, edge-vertex Szeged, total-Szeged, Padmakar-Ivan, Schultz, Gutman, Randic, generalized Randic, reciprocal Randic, reduced reciprocal Randic, first Zagreb, second Zagreb, reduced second Zagreb, hyper Zagreb, augmented Zagreb, atom-bond connectivity, harmonic, sum-connectivity, and geometric-arithmetic indices In addition we have obtained expressions for these topological indices for 3 types of parallelogram-like polycyclic benzenoid networks

Analytical expressions for topological properties of polycyclic benzenoid networks

Mostar indices of carbon nanostructures and circumscribed donut benzenoid systems

Unique and outstanding physiochemical properties of zeolite materials make them extremely useful in a variety of applications which offer a great potential for the development of material science. ...

Joseph Clement

Papers

Topological Indices and Their Applications to Circumcised Donut Benzenoid Systems, Kekulenes and Drugs

Mostar indices of carbon nanostructures and circumscribed donut benzenoid systems

Weighted Mostar indices as measures of molecular peripheral shapes with applications to graphene, graphyne and graphdiyne nanoribbons.

Analytical expressions for topological properties of polycyclic benzenoid networks

Relativistic distance-based topological descriptors of Linde type A zeolites and their doped structures with very heavy elements