Journal of Applied Mathematics
Volume 2012 (2012), Article ID 510180, 16 pages
http://dx.doi.org/10.1155/2012/510180
Research Article

Graph Products and Its Applications in Mathematical Formulation of Structures

M. Nouri,1 S. Talatahari,2 and A. Salimi Shamloo3

1Department of Structural Engineering, Islamic Azad University, Shabestar Branch, Shabestar, Iran
2Marand Faculty of Engineering, University of Tabriz, Tabriz 51667 71719, Iran
3Department of Mathematics, Islamic Azad University, Shabestar Branch, Shabestar, Iran

Received 15 June 2012; Revised 15 October 2012; Accepted 16 October 2012

Academic Editor: C. Conca

Copyright © 2012 M. Nouri et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The first step in the analysis of a structure is to generate its configuration. Different means are available for this purpose. The use of graph products is an example of such tools. In this paper, the use of product graphs is extended for the formation of different types of structural models. Here weighted graphs are used as the generators and the connectivity properties of different models are expressed in terms of the properties of their generators through simple algebraic relationships. In this paper by using graph product concepts and spatial structured matrices, a new algebraic closed form is proposed for mathematical formulation and presentation of structures. For clarification some examples are included.