Print ISSN: 1681-6900

Online ISSN: 2412-0758

Keywords : Laplacian matrix

A General Formula for Characteristic Polynomials of Some Special Graphs

Nawras A. Alwan; Nadia M. G. Al-Saidi

Engineering and Technology Journal, 2016, Volume 34, Issue 5, Pages 638-650

The calculation of characteristic polynomials (Ch. Poly.) of graphs of any size, especially for the large number of vertices n is an extremely tedious problem if used the traditional methods, so in this paper, the general formulas of the characteristic polynomial of some graphs, such as, path, complete, circle and star graphs are introduced. It is constructed based on adjacency and Laplacian matrices. The efficiency of the proposed method is demonstrated in terms of complexity to show an improvement over traditional methods.

On Some Properties of Characteristics Polynomials of the Complete Graphs Kn

Nuha A. Rajab; Samaa F. Ibraheem; Eman H. Ouda

Engineering and Technology Journal, 2013, Volume 31, Issue 4, Pages 520-528

This paper discusses the properties of the characteristic polynomial of the complete graphs Kn, n=1, 2… respective to the adjacency matrices. Two different types of matrices, the adjacency matrix and the signless Laplacian matrix, are presented. A recurrence relation for computing the characteristic polynomials depending on the adjacency matrix is introduced. We deduce that the coefficients of the polynomials based on the two different matrices have a relationship with Pascal triangle. The coefficients are computed using Matlab program. Many other properties of these coefficients are discussed also.