On Laplacian energy of thorn graph of K_n

In the present work, the adjacency matrix, the energy and the Laplacian energy for a picture fuzzy graph/directed graph have been introduced along with their lower and the upper bounds. Further, in the selection problem of decision making, a methodology for the ranking of the available alternatives has been presented by utilizing the picture fuzzy graph and its energy/Laplacian energy. For the shake of demonstrating the implementation of the introduced methodology, the task of site selection for the hydropower plant has been carried out as an application. The originality of the introduced approach, comparative remarks, advantageous features and limitations have also been studied in contrast with intuitionistic fuzzy and Pythagorean fuzzy information.

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The minimum covering signless laplacian energy of graph

Journal of Physics Conference Series ◽

10.1088/1742-6596/1597/1/012031 ◽

2020 ◽

Vol 1597 ◽

pp. 012031

Author(s):

Kavita Permi ◽

H S Manasa ◽

M C Geetha

Keyword(s):

Laplacian Energy ◽

Signless Laplacian ◽

Energy Of Graph

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A novel intrinsic time–scale decomposition–graph signal processing–based characteristic extraction method for rotor–stator rubbing of aeroengine

Journal of Vibration and Control ◽

10.1177/1077546320985968 ◽

2021 ◽

pp. 107754632098596

Author(s):

Mingyue Yu

Keyword(s):

Signal Processing ◽

Autocorrelation Function ◽

Time Scale ◽

Energy Index ◽

Signal Processing Algorithm ◽

Intrinsic Time ◽

Graph Signal Processing ◽

Laplacian Energy ◽

Rotational Components ◽

Time Scale Decomposition

Intrinsic time-scale decomposition and graph signal processing are combined to effectively identify a rotor–stator rubbing fault. The vibration signal is decomposed into mutually independent rotational components, and then, the Laplacian energy index is obtained by the graph signal of the autocorrelation function of rotational components, and the signal is reconstructed by an autocorrelation function of each proper rotation (PR) component relative to smaller Laplacian energy index (less complexity). Finally, characteristics are extracted from rotor–stator rubbing faults in an aeroengine according to square demodulation spectrum of a reconstructed signal. To validate the effectiveness of the algorithm, a comparative analysis is made among traditional intrinsic time-scale decomposition algorithm, combination of intrinsic time-scale decomposition and autocorrelation function, and the proposed intrinsic time-scale decomposition–graph signal processing algorithm. Comparative result shows that the proposed intrinsic time-scale decomposition–graph signal processing algorithm is more precise and effective than the traditional intrinsic time-scale decomposition and intrinsic time-scale decomposition and autocorrelation function algorithms in extracting characteristic frequency and frequency multiplication of rotor–stator rubbing faults and can greatly reduce the number of noise components irrelevant to faults.

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Properties of Commuting Graphs over Semidihedral Groups

Symmetry ◽

10.3390/sym13010103 ◽

2021 ◽

Vol 13 (1) ◽

pp. 103

Author(s):

Tao Cheng ◽

Matthias Dehmer ◽

Frank Emmert-Streib ◽

Yongtao Li ◽

Weijun Liu

Keyword(s):

Spanning Trees ◽

Laplacian Spectrum ◽

Vertex Connectivity ◽

Laplacian Energy ◽

Number Of Spanning Trees

This paper considers commuting graphs over the semidihedral group SD8n. We compute their eigenvalues and obtain that these commuting graphs are not hyperenergetic for odd n≥15 or even n≥2. We further compute the Laplacian spectrum, the Laplacian energy and the number of spanning trees of the commuting graphs over SD8n. We also discuss vertex connectivity, planarity, and minimum disconnecting sets of these graphs and prove that these commuting graphs are not Hamiltonian.

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Color signless Laplacian energy of graphs

AKCE International Journal of Graphs and Combinatorics ◽

10.1016/j.akcej.2017.02.003 ◽

2017 ◽

Vol 14 (2) ◽

pp. 142-148 ◽

Cited By ~ 5

Author(s):

Pradeep G. Bhat ◽

Sabitha D’Souza

Keyword(s):

Laplacian Energy ◽

Signless Laplacian

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Laplacian Energy of Digraphs and a Minimum Laplacian Energy Algorithm

International Journal of Foundations of Computer Science ◽

10.1142/s0129054115500203 ◽

2015 ◽

Vol 26 (03) ◽

pp. 367-380 ◽

Cited By ~ 1

Author(s):

Xingqin Qi ◽

Edgar Fuller ◽

Rong Luo ◽

Guodong Guo ◽

Cunquan Zhang

Keyword(s):

Oriented Graph ◽

Laplacian Matrix ◽

Upper Bounds ◽

Spectral Graph Theory ◽

Extremal Graphs ◽

Lower And Upper Bounds ◽

Spectral Graph ◽

Laplacian Energy ◽

Energy Formula ◽

Matrix Formula

In spectral graph theory, the Laplacian energy of undirected graphs has been studied extensively. However, there has been little work yet for digraphs. Recently, Perera and Mizoguchi (2010) introduced the directed Laplacian matrix [Formula: see text] and directed Laplacian energy [Formula: see text] using the second spectral moment of [Formula: see text] for a digraph [Formula: see text] with [Formula: see text] vertices, where [Formula: see text] is the diagonal out-degree matrix, and [Formula: see text] with [Formula: see text] whenever there is an arc [Formula: see text] from the vertex [Formula: see text] to the vertex [Formula: see text] and 0 otherwise. They studied the directed Laplacian energies of two special families of digraphs (simple digraphs and symmetric digraphs). In this paper, we extend the study of Laplacian energy for digraphs which allow both simple and symmetric arcs. We present lower and upper bounds for the Laplacian energy for such digraphs and also characterize the extremal graphs that attain the lower and upper bounds. We also present a polynomial algorithm to find an optimal orientation of a simple undirected graph such that the resulting oriented graph has the minimum Laplacian energy among all orientations. This solves an open problem proposed by Perera and Mizoguchi at 2010.

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