The spectral radius of trees on k pendant vertices

By Baofeng Wu, E. Xiao, Yuan Hong. 2005

195 citations recorded by the source corpus.

Abstract In this paper 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.

Subfields: Computational Theory and Mathematics, Computer Networks and Communications, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/6c6e147c7552f821615114b09b9c47ceded87600

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In Computational Theory and Mathematics

In Computer Networks and Communications

In Geometry and Topology

Citations in the corpus

Skew-adjacency matrices of graphs (2012, methodology): “One of the standard techniques used to compare spectral radii of adjacency matrices is that of edge-switching [23].”
Spectral analogues of Erdős’ and Moon–Moser’s theorems on Hamilton cycles (2015, background): “The above operation of graphs, introduced by Kelmans [23], is called the Kelmans operation (See [22], p. 44) Wu, Xiao, and Hong [24] proved that the spectral radius of a connected graph increases under the Kelmans operation.”
Graphs for which the least eigenvalue is minimal, II (2008, background): “1 is based on the following lemmas, the first of which is taken from [6].”