scholarly journals On Harary energy and Reciprocal distance Laplacian energies1

2021 ◽  
Vol 2090 (1) ◽  
pp. 012102
Author(s):  
Macarena Trigo
Keyword(s):  
Lower Bound ◽  
Laplacian Energy ◽  
Signless Laplacian ◽  
The Absolute

Abstract Let G be an graph simple, undirected, connected and unweighted graphs. The Reciprocal distance energy of a graph G is equal to the sum of the absolute values of the reciprocal distance eigenvalues. In this work, we find a lower bound for the Harary energy, reciprocal distance Laplacian energy and reciprocal distance signless Laplacian energy of a graph. Moreover, we find relationship between the Harary energy and Reciprocal distance Laplacian energies.

Energy of m-Polar Fuzzy Digraphs

2020 ◽  
pp. 469-491 ◽  
Author(s):  
Muhammad Akram ◽  
Danish Saleem ◽  
Ganesh Ghorai
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Adjacency Matrix ◽  
Fuzzy Graph ◽  
Laplacian Energy ◽  
Signless Laplacian ◽  
Different Types ◽  
Matrix Eigenvalues

In this chapter, firstly some basic definitions like fuzzy graph, its adjacency matrix, eigenvalues, and its different types of energies are presented. Some upper bound and lower bound for the energy of this graph are also obtained. Then certain notions, including energy of m-polar fuzzy digraphs, Laplacian energy of m-polar fuzzy digraphs and signless Laplacian energy of m-polar fuzzy digraphs are presented. These concepts are illustrated with several example, and some of their properties are investigated.

The relation between the minimum edge dominating energy and the other energies

2020 ◽  
Vol 12 (06) ◽  
pp. 2050078
Author(s):  
Fateme Movahedi
Keyword(s):  
Line Graph ◽  
The Other ◽  
Laplacian Energy ◽  
Graph Energy ◽  
Signless Laplacian ◽  
The Absolute

Let [Formula: see text] be a graph of the order [Formula: see text] and size [Formula: see text]. The minimum edge dominating energy is defined as the sum of the absolute values of eigenvalues of the minimum edge dominating matrix of the graph [Formula: see text]. In this paper, we establish relations between the minimum edge dominating energy of a graph [Formula: see text] and the graph energy, the energy of the line graph, signless Laplacian energy of [Formula: see text].

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

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

scholarly journals Bounds on Energy and Laplacian Energy of Graphs

2017 ◽  
Vol 23 (2) ◽  
pp. 21-31
Author(s):  
Sridhara G ◽  
Rajesh Kanna
Keyword(s):  
Upper Bounds ◽  
Simple Graph ◽  
Laplacian Energy ◽  
Energy Of Graph ◽  
The Absolute

Let G be simple graph with n vertices and m edges. The energy E(G) of G, denotedby E(G), is dened to be the sum of the absolute values of the eigenvalues of G. Inthis paper, we present two new upper bounds for energy of a graph, one in terms ofm,n and another in terms of largest absolute eigenvalue and the smallest absoluteeigenvalue. The paper also contains upper bounds for Laplacian energy of graph.

scholarly journals Q-borderenergetic threshold graphs

2020 ◽  
Vol 42 ◽  
pp. e91
Author(s):  
João Roberto Lazzarin ◽  
Oscar Franscisco Másquez Sosa ◽  
Fernando Colman Tura
Keyword(s):  
Complete Graph ◽  
Threshold Graphs ◽  
Laplacian Energy ◽  
Signless Laplacian

A graph G is said to be borderenergetic (L-borderenergetic, respectively) if its energy (Laplacian energy, respectively) equals the energy (Laplacian energy, respectively) of the complete graph. Recently, this concept was extend to signless Laplacian energy (see Tao, Q., Hou, Y. (2018). Q-borderenergetic graphs. AKCE International Journal of Graphs and Combinatorics). A graph G is called Q-borderenergetic if its signless Laplacian energy is the same of the complete graph Kn; i.e., QE(G) = QE(Kn) = 2n - 2: In this paper, we investigate Q-borderenergetic graphs on the class of threshold graphs. For a family of threshold graphs of order n = 100; we find out exactly 13 graphs such that QE(G) = 2n- 2:

scholarly journals An Intuitionistic Fuzzy Graph’s Signless Laplacian Energy

2018 ◽  
Vol 7 (4.10) ◽  
pp. 892
Author(s):  
Obbu Ramesh ◽  
S. Sharief Basha
Keyword(s):  
Adjacency Matrix ◽  
Fuzzy Graph ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Graphs ◽  
Laplacian Energy ◽  
Signless Laplacian ◽  
Intuitionistic Fuzzy Graphs

We are extending concept into the Intuitionistic fuzzy graph’ Signless Laplacian energy  instead of the Signless Laplacian energy of fuzzy graph. Now we demarcated an Intuitionistic fuzzy graph’s Signless adjacency matrix and also  an Intuitionistic fuzzy graph’s Signless Laplacian energy. Here we find the Signless Laplacian energy ‘s Intuitionistic fuzzy graphs above and below   boundaries of   an with suitable examples.   

scholarly journals On the Adjacency, Laplacian, and Signless Laplacian Spectrum of Coalescence of Complete Graphs

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
S. R. Jog ◽  
Raju Kotambari
Keyword(s):  
Line Graph ◽  
Laplacian Matrix ◽  
Spectral Graph Theory ◽  
Complete Graphs ◽  
Laplacian Spectrum ◽  
Spectral Graph ◽  
Signless Laplacian Spectrum ◽  
Subdivision Graph ◽  
Laplacian Energy ◽  
Signless Laplacian

Coalescence as one of the operations on a pair of graphs is significant due to its simple form of chromatic polynomial. The adjacency matrix, Laplacian matrix, and signless Laplacian matrix are common matrices usually considered for discussion under spectral graph theory. In this paper, we compute adjacency, Laplacian, and signless Laplacian energy (Qenergy) of coalescence of pair of complete graphs. Also, as an application, we obtain the adjacency energy of subdivision graph and line graph of coalescence from itsQenergy.

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