APPLICATIONS OF THE MATRIX PACKAGE MATLAB IN COMPUTING THE HOSOYA POLYNOMIAL OF Zig−Zag NANOTUBES

Nanostructured materials have received a lot of attention because of their novel properties. Nanotubes are an important category of one-dimensional nanostructured materials can be prepared from carbon. A topological index is a real number that is derived from molecular graphs of chemical compounds. Such numbers based on the distances in a graph are widely used for establishing relationships between the structure of molecules and their physico-chemical properties. The distance between atoms of a molecular graph is the length of a minimal path connecting them. The Wiener index was the first distance based topological index introduced early by Harold Wiener. It is defined as the sum of distances between any two carbon atoms in the molecules, in terms of carbon-carbon bonds. We encourage the reader to consult papers and references therein, for further study on the topic. We now recall some algebraic notations that will be used in the paper. Suppose G is a graph and e is an edge of G. If e connects the vertices u and v then we write e = uv. Let d(u,v) denote the distance between vertices u and v in G. The Hosoya polynomial of G is defined as where the sum is over all unordered pairs {u,v} of distinct vertices