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On the Laplacian spectral radius of trees with fixed diameter. (English) Zbl 1118.05063

The author considers the trees on \(n\) vertices with diameter \(d\), ordered by the largest eigenvalue of the Laplacian matrix, and determines the first \(\left\lfloor\frac d2\right\rfloor+1\) trees in this order. For an analogous result on ordering these trees by the largest eigenvalue of the adjacency matrix, see the paper by the author and J.-Y. Shao [Linear Algebra Appl. 413, 131-147 (2006; Zbl 1082.05060)].

MSC:

05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
05C12 Distance in graphs

Citations:

Zbl 1082.05060
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References:

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