The signless Laplacian spectral radius of tricyclic graphs and trees with k pendant vertices

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Abstract

In this paper, we consider the following problem: of all tricyclic graphs or trees of order n with k pendant vertices (n,k fixed), which achieves the maximal signless Laplacian spectral radius? We determine the graph with the largest signless Laplacian spectral radius among all tricyclic graphs with n vertices and k pendant vertices. Then we show that the maximal signless Laplacian spectral radius among all trees of order n with k pendant vertices is obtained uniquely at Tn,k, where Tn,k is a tree obtained from a star K1,k and k paths of almost equal lengths by joining each pendant vertex to one end-vertex of one path. We also discuss the signless Laplacian spectral radius of Tn,k and give some results. © 2011 Elsevier Inc. All rights reserved.

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Li, K., Wang, L., & Zhao, G. (2011). The signless Laplacian spectral radius of tricyclic graphs and trees with k pendant vertices. Linear Algebra and Its Applications, 435(4), 811–822. https://doi.org/10.1016/j.laa.2011.02.002

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