Volume 4, Issue 1 (3-2014)
2014, 4(1): 121-135 |
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Rahami H, Kaveh A. NUMBER OF SPANNING TREES FOR DIFFERENT PRODUCT GRAPHS. International Journal of Optimization in Civil Engineering 2014; 4 (1) :121-135
URL: http://ijoce.iust.ac.ir/article-1-166-en.html
URL: http://ijoce.iust.ac.ir/article-1-166-en.html
Abstract: (20593 Views)
In this paper simple formulae are derived for calculating the number of spanning trees of different product graphs. The products considered in here consists of Cartesian, strong Cartesian, direct, Lexicographic and double graph. For this purpose, the Laplacian matrices of these product graphs are used. Form some of these products simple formulae are derived and whenever direct formulation was not possible, first their Laplacian matrices are transformed into single block diagonal forms and then using the concept of determinant, the calculations are performed.
Keywords: Graph product, Cartesian, strong Cartesian, direct, lexicographic, double graph, spanning trees, Laplacian matrix, determinant, eigenvalues
Type of Study: Research |
Subject:
Applications
Received: 2014/04/11 | Accepted: 2014/04/11 | Published: 2014/04/11
Received: 2014/04/11 | Accepted: 2014/04/11 | Published: 2014/04/11
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