Signless Laplacian Spectral Conditions for Hamiltonicity of Graphs

Yu, Guidong; Miao-lin, YE; Cai, Gaixiang; Cao, Jinde

doi:10.1155/2014/282053

Cited by 16 publications

(6 citation statements)

References 12 publications

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“…Recently, Chen et al [37], Yu et al [178], and Wei et al [169] independently showed the spectral version of Hamilton-connectedness for graphs with large minimum degree. In 2020, Zhou, Wang and Lu [199] presented the signless Laplacian spectral conditions for Hamilton-connected graphs with large minimum degree.…”

Section: Problem For K-edge-connectivitymentioning

confidence: 99%

A survey on spectral conditions for some extremal graph problems

Li,

Liu,

Feng

2021

Preprint

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This survey is two-fold. We first report new progress on the spectral extremal results on the Turán type problems in graph theory. More precisely, we shall summarize the spectral Turán function in terms of the adjacency spectral radius and the signless Laplacian spectral radius for various graphs. For instance, the complete graphs, general graphs with chromatic number at least three, complete bipartite graphs, odd cycles, even cycles, color-critical graphs and intersecting triangles.The second goal is to conclude some recent results of the spectral conditions on some graphical properties. By a unified method, we present some sufficient conditions based on the adjacency spectral radius and the signless Laplacian spectral radius for a graph to be Hamiltonian, k-Hamiltonian, k-edge-Hamiltonian, traceable, k-pathcoverable, k-connected, k-edge-connected, Hamilton-connected, perfect matching and β-deficient.

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Section: Problem For K-edge-connectivitymentioning

confidence: 99%

A survey on spectral conditions for some extremal graph problems

Li,

Liu,

Feng

2021

Preprint

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“…Fiedler and Nikiforov [9] firstly gave sufficient conditions in terms of the spectral radius of a graph or its complement for the existence of Hamilton cycles. This work motivated further research, one may refer to [1,18,19,23,26,27,28,30]. Recently, by imposing the minimum degree of a graph as a new parameter, Li and Ning [14,15] extended some the results in [9,18,23].…”

Section: Introductionmentioning

confidence: 99%

Sufficient conditions for Hamilton-connected graphs in terms of (signless Laplacian) spectral radius

Zhou

Wang

2020

Linear Algebra and its Applications

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“…In 2010, Fiedler and Nikiforov [7] gave sufficient conditions on spectral radius for the existence of Hamilton cycles. Motivated by this, there are many other spectral conditions for the Hamiltonicity of graphs, one may refer to [1,14,15,16,19,20,21,22,23]. Recently, by imposing the minimum degree of a graph as a new parameter, Li and Ning [12,13] extended some the results in [7,14,16].…”

Section: Introductionmentioning

confidence: 99%