Laplacian Energy of a Complex Neutrosophic Graph

2018 ◽  
pp. 203-232 ◽  
Author(s):  
Mohsin Khan ◽  
Sadaf Umar ◽  
Said Broumi
Keyword(s):  
Laplacian Energy ◽  
Neutrosophic Graph

scholarly journals Novel Concept of Energy in Bipolar Single-Valued Neutrosophic Graphs with Applications

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 172
Author(s):  
Siti Nurul Fitriah Mohamad ◽  
Roslan Hasni ◽  
Florentin Smarandache ◽  
Binyamin Yusoff
Keyword(s):  
Renewable Energy Sources ◽  
Real Life ◽  
Energy Research ◽  
Neutrosophic Sets ◽  
Life Problems ◽  
Laplacian Energy ◽  
Graph Energy ◽  
Signless Laplacian ◽  
Neutrosophic Graph ◽  
Novel Concept

The energy of a graph is defined as the sum of the absolute values of its eigenvalues. Recently, there has been a lot of interest in graph energy research. Previous literature has suggested integrating energy, Laplacian energy, and signless Laplacian energy with single-valued neutrosophic graphs (SVNGs). This integration is used to solve problems that are characterized by indeterminate and inconsistent information. However, when the information is endowed with both positive and negative uncertainty, then bipolar single-valued neutrosophic sets (BSVNs) constitute an appropriate knowledge representation of this framework. A BSVNs is a generalized bipolar fuzzy structure that deals with positive and negative uncertainty in real-life problems with a larger domain. In contrast to the previous study, which directly used truth and indeterminate and false membership, this paper proposes integrating energy, Laplacian energy, and signless Laplacian energy with BSVNs to graph structure considering the positive and negative membership degree to greatly improve decisions in certain problems. Moreover, this paper intends to elaborate on characteristics of eigenvalues, upper and lower bound of energy, Laplacian energy, and signless Laplacian energy. We introduced the concept of a bipolar single-valued neutrosophic graph (BSVNG) for an energy graph and discussed its relevant ideas with the help of examples. Furthermore, the significance of using bipolar concepts over non-bipolar concepts is compared numerically. Finally, the application of energy, Laplacian energy, and signless Laplacian energy in BSVNG are demonstrated in selecting renewable energy sources, while optimal selection is suggested to illustrate the proposed method. This indicates the usefulness and practicality of this proposed approach in real life.

On Laplacian energy of picture fuzzy graphs in site selection problem

2021 ◽  
pp. 1-18
Author(s):  
Mahima Poonia ◽  
Rakesh Kumar Bajaj
Keyword(s):  
Decision Making ◽  
Site Selection ◽  
Upper Bounds ◽  
Selection Problem ◽  
Hydropower Plant ◽  
Fuzzy Graph ◽  
Fuzzy Information ◽  
Fuzzy Graphs ◽  
Laplacian Energy ◽  
Selection For

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.

scholarly journals The minimum covering signless laplacian energy of graph

2020 ◽  
Vol 1597 ◽  
pp. 012031
Author(s):  
Kavita Permi ◽  
H S Manasa ◽  
M C Geetha
Keyword(s):  
Laplacian Energy ◽  
Signless Laplacian ◽  
Energy Of Graph

Some operations on Dombi neutrosophic graph

2021 ◽  
Author(s):  
Tejinder Singh Lakhwani ◽  
Kartick Mohanta ◽  
Arindam Dey ◽  
Sankar Prasad Mondal ◽  
Anita Pal
Keyword(s):  
Neutrosophic Graph

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

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.

A neutrosophic folding and a neutrosophic retraction on a single-valued neutrosophic graph

2021 ◽  
pp. 1-7
Author(s):  
M. Abu Saleem
Keyword(s):  
And Topology ◽  
Neutrosophic Graph ◽  
The Relationship

The main aim of this article is to present neutrosophic folding and neutrosophic retractions on a single-valued neutrosophic graph Ğ from the viewpoint of geometry and topology. For this reason, we use a sequence of neutrosophic transformations on Ğ to obtain a new single-valued neutrosophic graph G ˇ 1 which contains different parameters under new conditions. We deduce the isometric neutrosophic folding on neutrosophic spheres and neutrosophic torii. Also, we determine the relationship between the limit neutrosophic folding and the limit of neutrosophic retraction on Ğ. Theorems regulating these relations are attained.

scholarly journals Properties of Commuting Graphs over Semidihedral Groups

Symmetry ◽  
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.

scholarly journals Color signless Laplacian energy of graphs

2017 ◽  
Vol 14 (2) ◽  
pp. 142-148 ◽  
Author(s):  
Pradeep G. Bhat ◽  
Sabitha D’Souza
Keyword(s):  
Laplacian Energy ◽  
Signless Laplacian

Laplacian Energy of Digraphs and a Minimum Laplacian Energy Algorithm

2015 ◽  
Vol 26 (03) ◽  
pp. 367-380 ◽  
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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