Laplacian Estrada and Normalized Laplacian Estrada Indices of Evolving Graphs

Shang, Yilun

doi:10.1371/journal.pone.0123426

Cited by 30 publications

(23 citation statements)

References 41 publications

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“…In [22] the author went further and considered the dynamic Laplacian Estrada index and the dynamic normalized Laplacian Estrada index. He showed that it is possible to define dynamic (normalized) Laplacian Estrada index in full analogy with dynamic Estrada index [27].…”

Section: Future Directions and Conclusionmentioning

confidence: 99%

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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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Section: Future Directions and Conclusionmentioning

confidence: 99%

“…Moreover, we have come across an article concerning evolving graphs as suggested by the anonymous referee in [27,22]. In those articles the authors have defined an evolving graph G 1 , G 2 , .…”

Section: Future Directions and Conclusionmentioning

confidence: 99%

On some aspects of the generalized Petersen graph

Yegnanarayanan

2017

ejgta

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“…The Estrada indices have also found a range of applications in chemistry and complex networks. These days, a dynamic version of the Estrada indices are proposed [12] to study large-scale time-evolving networks which arise naturally in a variety of areas from peer-to-peer telecommunication to online human social behavior to neuroscience.…”

Section: Introductionmentioning

confidence: 99%

Discrete Differential Geometry and the Structural Study of Protein Complexes

Morikawa¹

2017

OJDM

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This paper proposes a novel four-dimensional approach to the structural study of protein complexes. In the approach, the surface of a protein molecule is to be described using the intersection of a pair of four-dimensional triangular cones (with multiple top vertexes). As a mathematical toy model of protein complexes, we consider complexes of closed trajectories of n-simplices ( 2,3, 4, n =  ), where the design problem of protein complexes corresponds to an extended version of the Hamiltonian cycle problem. The problem is to find "a set of" closed trajectories of n-simplices which fills the n -dimensional region defined by a given pair of 1 n + -dimensional triangular cones. Here we give a solution to the extended Hamiltonian cycle problem in the case of 2 n = using the discrete differential geometry of triangles (i.e., 2-simplices).

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“…Many properties of LEE, including upper/lower bounds and extremal graphs, have been established (see e.g. [15,[17][18][19][20] …”

Section: Introductionmentioning

confidence: 99%

On the number of spanning trees, the Laplacian eigenvalues, and the Laplacian Estrada index of subdivided-line graphs

Shang

2016

Open Mathematics

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As a generalization of the Sierpiński-like graphs, the subdivided-line graph .G/ of a simple connected graph G is defined to be the line graph of the barycentric subdivision of G. In this paper we obtain a closed-form formula for the enumeration of spanning trees in .G/, employing the theory of electrical networks. We present bounds for the largest and second smallest Laplacian eigenvalues of .G/ in terms of the maximum degree, the number of edges, and the first Zagreb index of G. In addition, we establish upper and lower bounds for the Laplacian Estrada index of .G/ based on the vertex degrees of G. These bounds are also connected with the number of spanning trees in .G/.

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Laplacian Estrada and Normalized Laplacian Estrada Indices of Evolving Graphs

Cited by 30 publications

References 41 publications

On some aspects of the generalized Petersen graph

On some aspects of the generalized Petersen graph

Discrete Differential Geometry and the Structural Study of Protein Complexes

On the number of spanning trees, the Laplacian eigenvalues, and the Laplacian Estrada index of subdivided-line graphs

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