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On the characteristic and Laplacian polynomials of trees

✍ Scribed by Abbas Heydari; Bijan Taeri

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
232 KB
Volume
432
Category
Article
ISSN
0024-3795

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✦ Synopsis

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 Laplacian matrix for some balanced trees, Linear Algebra Appl. 403 (2005) 97-117] on a special class of rooted unweighted trees, namely the trees such that their vertices in the same level have equal degrees.

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On the Laplacian spectral radius of a tr
On the Laplacian spectral radius of a tree
✍ Ji-Ming Guo πŸ“‚ Article πŸ“… 2003 πŸ› Elsevier Science 🌐 English βš– 84 KB

Let G be a graph; its Laplacian matrix is the difference of the diagonal matrix of its vertex degrees and its adjacency matrix. In this paper, we present a sharp upper bound for the Laplacian spectral radius of a tree in terms of the matching number and number of vertices, and deduce from that the l