Ordering trees by their largest eigenvalues
نویسندگان
چکیده
منابع مشابه
Ordering trees with n vertices and matching number q by their largest Laplacian eigenvalues
Denote by Tn,q the set of trees with n vertices and matching number q. Guo [On the Laplacian spectral radius of a tree, Linear Algebra Appl. 368 (2003) 379–385] gave the tree in Tn,q with the greatest value of the largest Laplacian eigenvalue. In this paper, we give another proof of this result. Using our method, we can go further beyond Guo by giving the tree in Tn,q with the second largest va...
متن کاملOrdering trees by their Laplacian spectral radii
Denote by Tn the set of trees on n vertices. Zhang and Li [X.D. Zang, J.S. Li, The two largest eigenvalues of Laplacian matrices of trees (in Chinese), J. China Univ. Sci. Technol. 28 (1998) 513–518] and Guo [J.M. Guo, On the Laplacian spectral radius of a tree, Linear Algebra Appl. 368 (2003) 379–385] give the first four trees in Tn, ordered according to their Laplacian spectral radii. In this...
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It is now believed that the limiting distribution function of the largest eigenvalue in the three classic random matrix models GOE, GUE and GSE describe new universal limit laws for a wide variety of processes arising in mathematical physics and interacting particle systems. These distribution functions, expressed in terms of a certain Painlevé II function, are described and their occurences su...
متن کاملOrdering Trees with Perfect Matchings by Their Wiener Indices
The Wiener index of a connected graph is the sum of all pairwise distances of vertices of the graph. In this paper, we consider the Wiener indices of trees with perfect matchings, characterizing the eight trees with smallest Wiener indices among all trees of order 2 ( 11) m m with perfect matchings.
متن کاملOrdering Unicyclic Graphs in Terms of Their Smaller Least Eigenvalues
Let G be a simple graph with n vertices, and let A be the 0, 1 -adjacency matrix of G. We call det λI −A the characteristic polynomial of G, denoted by P G; λ , or abbreviated P G . Since A is symmetric, its eigenvalues λ1 G , λ2 G , . . . , λn G are real, and we assume that λ1 G ≥ λ2 G ≥ · · · ≥ λn G . We call λn G the least eigenvalue of G. Up to now, some good results on the least eigenvalue...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2003
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(03)00384-7