Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: A new algorithm for computing distance matrix and Wiener index of zig-zag polyhex nanotubes | Nanoscale Res Lett 2007 2 202-206 DOI s11671-007-9051-y NANO EXPRESS A new algorithm for computing distance matrix and Wiener index of zig-zag polyhex nanotubes Ali Reza Ashrafi Shahram Yousefi Received 31 December 2006 Accepted 20 February 2007 Published online 10 April 2007 to the authors 2007 Abstract The Wiener index of a graph G is defined as the sum of all distances between distinct vertices of G. In this paper an algorithm for constructing distance matrix of a zig-zag polyhex nanotube is introduced. As a consequence the Wiener index of this nanotube is computed. Keywords Zig-zag polyhex nanotube Distance matrix Wiener index Introduction Carbon nanotubes form an interesting class of carbon nanomaterials. These can be imagined as rolled sheets of graphite about different axes. These are three types of nanotubes armchair chiral and zigzag structures. Further nanotubes can be categorized as single-walled and multiwalled nanotubes and it is very difficult to produce the former. Graph theory has found considerable use in chemistry particularly in modeling chemical structure. Graph theory has provided the chemist with a variety of very useful tools namely the topological index. A topological index is a numeric quantity that is mathematically derived in a direct and unambiguous manner from the structural graph of a molecule. It has been found that many properties of a A. R. Ashrafi H Institute for Nanoscience and Nanotechnology University of Kashan Kashan Iran e-mail ashrafi@ S. Yousefi Center for Space Studies Malek-Ashtar University of Technology Tehran Iran chemical compound are closely related to some topological indices of its molecular graph 1 2 . Among topological indices the Wiener index 3 is probably the most important one. This index was introduced by the chemist H. Wiener about 60 years ago to demonstrate correlations between physico-chemical properties of organic compounds and the topological structure of their molecular graphs. .
