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On Some Properties of Characteristics Polynomials of the Complete Graphs Kn | ||
| Engineering and Technology Journal | ||
| Article 10, Volume 31, 4 B, 2013, Pages 520-528 PDF (570.7 K) | ||
| DOI: 10.30684/etj.31.4B.10 | ||
| Authors | ||
| Nuha A. Rajab; Samaa F. Ibraheem; Eman H. Ouda | ||
| Abstract | ||
| 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. | ||
| Keywords | ||
| Laplacian matrix; Pascal triangle; Complete graph | ||
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