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Mathematical Problems in Engineering
Volume 2014, Article ID 613685, 5 pages
Research Article

The Number of Spanning Trees in the Composition Graphs

Feng Li1,2,3

1College of Computer Science, Qinghai Normal University, Xi’ning 810003, China
2Institute of Information and System Sciences, School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China
3Ministry of Education Key Lab for Intelligent Networks and Network Security, Xi’an Jiaotong University, Xi’an 710049, China

Received 4 October 2013; Accepted 10 February 2014; Published 19 March 2014

Academic Editor: J. J. Judice

Copyright © 2014 Feng Li. 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.


Using the composition of some existing smaller graphs to construct some large graphs, the number of spanning trees and the Laplacian eigenvalues of such large graphs are also closely related to those of the corresponding smaller ones. By using tools from linear algebra and matrix theory, we establish closed formulae for the number of spanning trees of the composition of two graphs with one of them being an arbitrary complete 3-partite graph and the other being an arbitrary graph. Our results extend some of the previous work, which depend on the structural parameters such as the number of vertices and eigenvalues of the small graphs only.