On the ordering of trees by the Laplacian coefficients
✍ Scribed by Aleksandar Ilić
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 212 KB
- Volume
- 431
- 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
Let G be a graph of order n and let (G, λ) = n k=0 (-1) k c k λ n-k be the characteristic polynomial of its Laplacian matrix. Zhou and Gutman recently proved that among all trees of order n, the kth coefficient c k is largest when the tree is a path, and is smallest for stars. A new proof and a stre