The Normalized Laplacian Estrada Index of Graphs

Hakimi-Nezhaad, Mardjan; Hua, Hongbo; Ашрафи, Али Реза; Suxiang, Qian

doi:10.14317/jami.2014.227

Cited by 4 publications

(8 citation statements)

References 14 publications

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“…Similarly as commented at the end of the above section, for the static case of N = 1, some bounds for the normalized Laplacian Estrada index are reported in the literature by involving more complicated graph-theoretic parameters, including normalized Laplacian energy [ 22 ], and the Randic index [ 35 , 51 ], which are a bit cumbersome when large-scale network applications are taken into account.…”

Section: Resultsmentioning

confidence: 97%

“…The normalized Laplacian Estrada index is put forward in [ 35 ] as See also [ 22 ] for an essentially equivalent definition. ℒ EE ( G ) has been addressed for a class of tree-like fractals [ 36 ].…”

Section: Resultsmentioning

confidence: 99%

“…This condition is equivalent to

, which contradicts the assumption. Theorem 3.4 in [ 35 ] can be reproduced by setting N = 1.…”

Section: Resultsmentioning

confidence: 99%

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Laplacian Estrada and Normalized Laplacian Estrada Indices of Evolving Graphs

Shang

2015

PLoS ONE

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Large-scale time-evolving networks have been generated by many natural and technological applications, posing challenges for computation and modeling. Thus, it is of theoretical and practical significance to probe mathematical tools tailored for evolving networks. In this paper, on top of the dynamic Estrada index, we study the dynamic Laplacian Estrada index and the dynamic normalized Laplacian Estrada index of evolving graphs. Using linear algebra techniques, we established general upper and lower bounds for these graph-spectrum-based invariants through a couple of intuitive graph-theoretic measures, including the number of vertices or edges. Synthetic random evolving small-world networks are employed to show the relevance of the proposed dynamic Estrada indices. It is found that neither the static snapshot graphs nor the aggregated graph can approximate the evolving graph itself, indicating the fundamental difference between the static and dynamic Estrada indices.

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Section: Resultsmentioning

confidence: 97%

Section: Resultsmentioning

confidence: 99%

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Laplacian Estrada and Normalized Laplacian Estrada Indices of Evolving Graphs

Shang

2015

PLoS ONE

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“…The authors in [15] have introduced another variation to Estrada index namely normalized Laplacian Estrada index. For fundamental properties of EE one can also see [19], The normalized Laplacian matrix (G) = ( ij ) p×p where ij = 1 if i = j and deg…”

Section: Normalized Estrada Indexmentioning

confidence: 99%

“…This is one of the main reasons that motivated us to look at the generalized Petersen graph. Also see [4,30,18,1,15,19,6,7]. …”

Section: Normalized Estrada Indexmentioning

confidence: 99%

On some aspects of the generalized Petersen graph

Yegnanarayanan

2017

ejgta

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Let p ≥ 3 be a positive integer and let k ∈ {1, 2, . . . p − 1}\ p/2 . The generalized Petersen graph GP ((p, k) has its vertex and edge set asIn this paper we probe its spectrum and determine the Estrada index, Laplacian Estrada index, signless Laplacian Estrada index, normalized Laplacian Estrada index, and energy of a graph. While obtaining some interesting results, we also provide relevant background and problems.

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The many facets of the Estrada indices of graphs and networks

Estrada

2021

SeMA

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The Estrada index of a graph/network is defined as the trace of the adjacency matrix exponential. It has been extended to other graph-theoretic matrices, such as the Laplacian, distance, Seidel adjacency, Harary, etc. Here, we describe many of these extensions, including new ones, such as Gaussian, Mittag–Leffler and Onsager ones. More importantly, we contextualize all of these indices in physico-mathematical frameworks which allow their interpretations and facilitate their extensions and further studies. We also describe several of the bounds and estimations of these indices reported in the literature and analyze many of them computationally for small graphs as well as large complex networks. This article is intended to formalize many of the Estrada indices proposed and studied in the mathematical literature serving as a guide for their further studies.

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The Normalized Laplacian Estrada Index of Graphs

Cited by 4 publications

References 14 publications

Laplacian Estrada and Normalized Laplacian Estrada Indices of Evolving Graphs

Laplacian Estrada and Normalized Laplacian Estrada Indices of Evolving Graphs

On some aspects of the generalized Petersen graph

The many facets of the Estrada indices of graphs and networks

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