给定独立数的树的最大拉普拉斯谱半径
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摘要
图的拉普拉斯矩阵最大特征值定义为图的拉普拉斯谱半径,它是刻画图结构性质的重要参数。本文主要介绍了在所有给定独立数为α的n阶树中具有最大拉普拉斯谱半径的唯一极图,其中[|n/2|]≤α≤(n-1)。
The Laplacian spectral radius of a graph is defined as the largest eigenvalues of the Laplacian matrix of the graph, which is an important algebraic parameter on characterizing structural property of graphs. In this paper, we characterize the graph with maximal Laplacian spectral radius among all the trees with n vertices and independence number for [|n/2|]≤ α ≤( n-1).
The Laplacian spectral radius of a graph is defined as the largest eigenvalues of the Laplacian matrix of the graph, which is an important algebraic parameter on characterizing structural property of graphs. In this paper, we characterize the graph with maximal Laplacian spectral radius among all the trees with n vertices and independence number for [|n/2|]≤ α ≤( n-1).
引文
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[2]FENG L,SONG J.Spectral radius of unicyclic graphs with given independence number[J].Util Math,2011,84:33-43.
[3]GUO J M,SHAO J Y.On the spectral radius of trees with fixed diameter[J].Linear Algebra Appl,2006,413:131-147.
[4]HONG Y,ZHANG X D.Sharp upper and lower bounds for largest eigenvalue of the Laplacian matrices of trees[J].Discrete Math,2005,296:187-197.
[5]HOU Y P,LI J S.Bounds on the largest eigenvalues of trees with a given size of matching[J].Linear Algebra Appl,2002,342:203-217.
[6]JI C Y,LU M.On the spectral radius of trees with given independence number[J].Linear Algebra Appl,2016,488:102-108.
[7]LU H,LIN Y.Maximum spectral radius of graphs with given connectivity,minimum degree and independence number[J].JDiscrete Algorithms,2015,31:113-119.
[8]XU M,HONG Y,SHU J,et al.The minimum spectral radius of graphs with a given independence number[J].Linear Algebra Appl,2009,431(5):937-945.