On the characteristic and Laplacian polynomials of trees |
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Authors: | Abbas Heydari |
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Institution: | 1. Department of Mathematics, Islamic Azad University, Arak 38135-567, Iran;2. Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran |
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Abstract: | 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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