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Mathematical Problems in Engineering
Volume 2013, Article ID 820549, 11 pages
http://dx.doi.org/10.1155/2013/820549
Research Article

On the Complexity of a Class of Pyramid Graphs and Chebyshev Polynomials

1Department of Mathematics, Faculty of Science, Taibah University, Al Madinah 344, Saudi Arabia
2Department of Mathematics, Faculty of Science, Minoufiya University, Shibin El Kom 32511, Egypt

Received 29 April 2013; Revised 26 September 2013; Accepted 2 October 2013

Academic Editor: Xiaojun Wang

Copyright © 2013 S. N. Daoud. 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

In mathematics, one always tries to get new structures from given ones. This also applies to the realm of graphs, where one can generate many new graphs from a given set of graphs. In this paper we define a class of pyramid graphs and derive simple formulas of the complexity, number of spanning trees, of these graphs, using linear algebra, Chebyshev polynomials, and matrix analysis techniques.