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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 965105, 23 pages
http://dx.doi.org/10.1155/2014/965105
Research Article

Number of Spanning Trees of Different Products of Complete and Complete Bipartite Graphs

1Department of Mathematics, Faculty of Science, Menoufia University, Shebin Elkom 32511, Egypt
2Department of Mathematics, Faculty of Science, Taibah University, Al Madinah 41411, Saudi Arabia

Received 28 December 2013; Revised 31 May 2014; Accepted 31 May 2014; Published 2 July 2014

Academic Editor: Efstratios Tzirtzilakis

Copyright © 2014 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

Spanning trees have been found to be structures of paramount importance in both theoretical and practical problems. In this paper we derive new formulas for the complexity, number of spanning trees, of some products of complete and complete bipartite graphs such as Cartesian product, normal product, composition product, tensor product, symmetric product, and strong sum, using linear algebra and matrix theory techniques.