Ordering of trees with fixed matching number by the Laplacian coefficients
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...
متن کاملOn the Signless Laplacian Spectral Radius of Unicyclic Graphs with Fixed Matching Number
We determine the graph with the largest signless Laplacian spectral radius among all unicyclic graphs with fixed matching number.
متن کاملOn the Coefficients of the Laplacian Characteristic Polynomial of Trees
k=0 (−1)n−k ck(T ) λk . Then, as well known, c0(T ) = 0 and c1(T ) = n . If T differs from the star (Sn) and the path (Pn), which requires n ≥ 5 , then c2(Sn) < c2(T ) < c2(Pn) and c3(Sn) < c3(T ) < c3(Pn) . If n = 4 , then c3(Sn) = c3(Pn) . AMS Mathematics Subject Classification (2000): 05C05, 05C12, 05C50
متن کاملThe Laplacian spectral radius of graphs with given matching number
In this paper, we show that of all graphs of order n with matching number β, the graphs with maximal spectral radius are Kn if n = 2β or 2β + 1; K2β+1 ∪Kn−2β−1 if 2β + 2 n < 3β + 2; Kβ ∨ Kn−β or K2β+1 ∪Kn−2β−1 if n = 3β + 2; Kβ ∨ Kn−β if n > 3β + 2, where Kt is the empty graph on t vertices. © 2006 Elsevier Inc. All rights reserved. AMS classification: 05C35; 05C50
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2011
ISSN: 0024-3795
DOI: 10.1016/j.laa.2011.02.050