The least eigenvalue of signless Laplacian of graphs under perturbation

Wang, Yi; Fan, Yi-Zheng

doi:10.1016/j.laa.2011.08.043

Cited by 31 publications

(26 citation statements)

References 17 publications

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“…Finally we present some upper bounds of the least eigenvalue and prove that zero is the least limit point of the least eigenvalues of connected non-odd-bipartite hypergraphs. The perturbation result on the least eigenvalue in this paper is a generalization of that on the least eigenvalue of the signless Laplacian matrix of a simple graph in [19].…”

Section: Introductionmentioning

confidence: 91%

The least eigenvalue of signless Laplacian of non-bipartite graphs with given domination number

Fan

Tan

2014

Discrete Mathematics

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Section: Introductionmentioning

confidence: 91%

The least eigenvalue of signless Laplacian of non-bipartite graphs with given domination number

Fan

Tan

2014

Discrete Mathematics

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“…Lemma 2.2 [15] Let G be a connected graph which contains a bipartite branch H with root v s , and let X be an eigenvector of G corresponding to q min (G).…”

Section: Lemma 21 [3]mentioning

confidence: 99%

Further results on the least Q-eigenvalue of a graph with fixed domination number

Zhai

2019

Linear and Multilinear Algebra

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In this paper, we proceed on determining the minimum q min among the connected nonbipartite graphs on n ≥ 5 vertices and with domination number n+1 3 < γ ≤ n−1 2 . Further results obtained are as follows:(i) among all nonbipartite connected graph of order n ≥ 5 and with domination number n−1 2 , the minimum q min is completely determined;(ii) among all nonbipartite graphs of order n ≥ 5, with odd-girth g o ≤ 5 and domination number at least n+1 3 < γ ≤ n−2 2 , the minimum q min is completely determined.

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“…Fan investigated the relations between the least signless Laplacian eigenvalue and some parameters reflecting the graph bipartiteness. In [10], Y. Wang and Y. Fan investigated the least signless Laplacian eigenvalue of a graph under some perturbations, and minimized the least eigenvalue of the signless Laplacian among the class of connected graphs with fixed order which contains a given nonbipartite graph as an induced subgraph.…”

Section: Elamentioning

confidence: 99%