Normalized Laplacian Eigenvalues and Energy of Trees
نویسندگان
چکیده
منابع مشابه
Eigenvalues of the normalized Laplacian
A graph can be associated with a matrix in several ways. For instance, by associating the vertices of the graph to the rows/columns and then using 1 to indicate an edge and 0 otherwise we get the adjacency matrix A. The combinatorial Laplacian matrix is defined by L = D − A where D is a diagonal matrix with diagonal entries the degrees and A is again the adjacency matrix. Both of these matrices...
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*Correspondence: [email protected] 1School of Mathematics and Statistics, Minnan Normal University, Zhangzhou, Fujian, P.R. China 2Center for Discrete Mathematics, Fuzhou University, Fuzhou, Fujian, P.R. China Full list of author information is available at the end of the article Abstract Let G be a simple connected graph of order n, where n≥ 2. Its normalized Laplacian eigenvalues are 0 = λ1 ...
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Limit points for the positive eigenvalues of the normalized Laplacian matrix of a graph are considered. Specifically, it is shown that the set of limit points for the j-th smallest such eigenvalues is equal to [0, 1], while the set of limit points for the j-th largest such eigenvalues is equal to [1, 2]. Limit points for certain functions of the eigenvalues, motivated by considerations for rand...
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The eigenvalues of the normalized Laplacian matrix of a network play an important role in its structural and dynamical aspects associated with the network. In this paper, we study the spectra and their applications of normalized Laplacian matrices of a family of fractal trees and dendrimers modeled by Cayley trees, both of which are built in an iterative way. For the fractal trees, we apply the...
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Here, we find the characteristics polynomial of normalized Laplacian of a tree. The coefficients of this polynomial are expressed by the higher order general Randić indices for matching, whose values depend on the structure of the tree. We also find the expression of these indices for starlike tree and a double-starlike tree, Hm(p, q). Moreover, we show that two cospectral Hm(p, q) of the same ...
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ژورنال
عنوان ژورنال: Taiwanese Journal of Mathematics
سال: 2016
ISSN: 1027-5487
DOI: 10.11650/tjm.20.2016.6668