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The spectral radius of trees on \(k\) pendant vertices. (English) Zbl 1057.05057

Summary: We consider the following problem: Of all trees of order \(n\) with \(k\) pendant vertices (\(n, k\) fixed), which achieves the maximal spectral radius? We show that the maximal spectral radius is obtained uniquely at \(T_{n,k}\), where \(T_{n,k}\) is a tree obtained from a star \(K_{1,k}\) and \(k\) paths of almost equal lengths by joining each pendant vertex of \(K_{1,k}\) to an end vertex of one path. We also discuss the spectral radius of \(T_{n,k}\) and get some results.

MSC:

05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
05C05 Trees
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References:

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