Distances in benzenoid systems: Further developments

Distances in benzenoid systems: Further developments

In this note we present some new results on distances in benzenoids. An algorithm is presented which, for a given benzenoid system G bounded by a simple circuit 2 with n vertices, computes the Wiener index of G in O(n) time. Also we show that benzenoid systems have a convenient dismantling scheme, which can be derived by applying breadth-first search to their dual graphs. Our last result deals ...

On Distances in Benzenoid Systems

We show that the molecular graph G of a benzenoid hydrocarbon admits an isometric embedding into the Cartesian product of three trees T1, T2, and T3 defined by three directions of the host hexagonal grid. Namely, to every vertex V of G one can associate an ordered triplet (V1, V2, V3) with Vi being a vertex of Ti (i ) 1, 2, 3), such that the graph-theoretic distance between two vertices u, V of...

Recent Developments in Discrete Event Systems

This article is a brief exposure of the process approach to a newly emerging area called "discrete event systems" in control theory and summarizes some of the recent developments in this area. Discrete event systems is an area of research that is developing within the interstices of computer, control and communication sciences. The basic direction of research addresses issues in the analysis an...

Further Developments in Dynamic Focusing

Dynamic focusing has been proposed[1] as a way to eliminate a conventional collimation and final focus system in linear colliders, and is a scheme that is more readily extended to colliders at several TeV center-of-mass energy. In this paper we examine several outstanding issues, in particular, the optimization of the lens and main beam parameters. Simulations of the lens-lens, lens-main, and m...

Further developments in psychogeriatrics in Britain.