The Laplacian spectrum of corona of two graphs

Li, Qun

doi:10.5937/kgjmath1401163l

Cited by 24 publications

(15 citation statements)

References 7 publications

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“…The proof of Theorem 4.2 is evident using methods in [22,23,29]. For convenience of the following discussion we give a similar proof here:…”

Section: Spectra Of Laplacian Matrixmentioning

confidence: 97%

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Corona graphs as a model of small-world networks

Lv¹,

Yi²,

Zhang³

2015

J. Stat. Mech.

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We introduce recursive corona graphs as a model of small-world networks. We investigate analytically the critical characteristics of the model, including order and size, degree distribution, average path length, clustering coefficient, and the number of spanning trees, as well as Kirchhoff index. Furthermore, we study the spectra for the adjacency matrix and the Laplacian matrix for the model. We obtain explicit results for all the quantities of the recursive corona graphs, which are similar to those observed in real-life networks.

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“…The proof of Theorem 4.2 is evident using methods in [22,23,29]. For convenience of the following discussion we give a similar proof here:…”

Section: Spectra Of Laplacian Matrixmentioning

confidence: 97%

“…Literatures about the corona product and its related graphs are partly established [22,23]. Let G = (V (G), E(G)) be the embedded graph of a network.…”

Section: Graph Constructionmentioning

confidence: 99%

Corona graphs as a model of small-world networks

Lv¹,

Yi²,

Zhang³

2015

J. Stat. Mech.

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“…, are the multiplicities of these eigenvalues. The spectrum can be also simply denoted by a sequence of eigenvalues (see [16,17,19]): ( ( )) = ( 1 , 2 , . .…”

Section: ⋅⋅⋅mentioning

confidence: 99%

“…Our findings bring a better perspective into the combination between consensus problems and the field of graph theory, and our work makes further efforts to use the theory of graph spectra for studying performance of consensus, where the "performance" in this article mainly refers to the convergence speed and robustness of consensus. Due to the chosen undirected graphs, we study the convergence speed and robustness of consensus to communication noise with an application of Laplacian spectrum of corona ( [16,17]) of two graphs, and find that the method of constructing networks by using the notion of corona of two graphs can generate a class of polymer small-world network ( [5]).…”

Section: Introductionmentioning

confidence: 99%

On Consensus of Star-Composed Networks with an Application of Laplacian Spectrum

Huang

Jiang

et al. 2017

Discrete Dynamics in Nature and Society

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In this paper, we mainly study the performance of star-composed networks which can achieve consensus. Specifically, we investigate the convergence speed and robustness of the consensus of the networks, which can be measured by the smallest nonzero eigenvalue λ2 of the Laplacian matrix and the H2 norm of the graph, respectively. In particular, we introduce the notion of the corona of two graphs to construct star-composed networks and apply the Laplacian spectrum to discuss the convergence speed and robustness for the communication network. Finally, the performances of the star-composed networks have been compared, and we find that the network in which the centers construct a balanced complete bipartite graph has the most advantages of performance. Our research would provide a new insight into the combination between the field of consensus study and the theory of graph spectra.

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“…[22] Let G 1 and G 2 be graphs of order n 1 and n 2 respectively. If Let G 1 and G 2 be graphs of order n 1 and n 2 respectively.…”

mentioning

confidence: 99%

Complexity of Join and Corona graphs and Chebyshev polynomials

Daoud

2018

Journal of Taibah University for Science

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Boesh and Prodinger have shown how to use properties of Chebyshev polynomials to compute formulas for the number of spanning trees of some special graphs. In this paper, we extend this idea for some operations on graphs such as, Join and Corona of two graphs G 1 and G 2 , if G 1 and G 2 are one of the following graphs: (i) Path graph P n , (ii) Cycle graph C n , (iii) Complete graph K n , (iv) Complete bipartite K m, n , (v) Hypercube graph Q n , (vi) Fan graph F n and (vi) Wheel graph W n .

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The Laplacian spectrum of corona of two graphs

Cited by 24 publications

References 7 publications

Corona graphs as a model of small-world networks

Corona graphs as a model of small-world networks

On Consensus of Star-Composed Networks with an Application of Laplacian Spectrum

Complexity of Join and Corona graphs and Chebyshev polynomials

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