On the spectral radius of trees with given independence number
نویسندگان
چکیده
منابع مشابه
Trees with given maximum degree minimizing the spectral radius
The spectral radius of a graph is the largest eigenvalue of the adjacency matrix of the graph. Let T (n,∆, l) be the tree which minimizes the spectral radius of all trees of order n with exactly l vertices of maximum degree ∆. In this paper, T (n,∆, l) is determined for ∆ = 3, and for l ≤ 3 and n large enough. It is proven that for sufficiently large n, T (n, 3, l) is a caterpillar with (almost...
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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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The independence number of a graph is defined as the maximum size of a set of pairwise non-adjacent vertices and the spectral radius is defined as the maximum eigenvalue of the adjacency matrix of the graph. Xu et al. in [The minimum spectral radius of graphs with a given independence number, Linear Algebra and its Applications 431 (2009) 937–945] determined the connected graphs of order n with...
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Article history: Received 17 March 2008 Accepted 9 October 2008 Available online 3 December 2008 Submitted by R.A. Brualdi AMS classification: 05C50
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There are 11 integral trees with largest eigenvalue 3.
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2016
ISSN: 0024-3795
DOI: 10.1016/j.laa.2015.09.030