Let \* 1 >\* 2 > } } } >\* d be points on the real line. For every k=1, 2, ..., d, the k-alternating polynomial P k is the polynomial of degree k and norm Because of this optimality property, these polynomials may be thought of as the discrete version of the Chebychev polynomials T k and, for parti
On the characteristic polynomial of a special class of graphs and spectra of balanced trees
β Scribed by Abbas Heydari; Bijan Taeri
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 262 KB
- Volume
- 429
- Category
- Article
- ISSN
- 0024-3795
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We find the characteristic polynomials of adjacency and Laplacian matrices of arbitrary unweighted rooted trees in term of vertex degrees, using the concept of the rooted product of graphs. Our result generalizes a result of Rojo and Soto [O. Rojo, R. Soto, The spectra of the adjacency matrix and La
Several unique advantages of the Le Verrier-Fadeev-Frame method for the characteristic polynomials of graphs over the method proposed by Zivkovic recently based on the Givens-Householder method are described. It is shown that the Givens-Householder method proposed by Zivkovic, by itself fails for di
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