scholarly journals Change in Semigraph Energy Due to Edge Deletion and its Relation with Distance Energy

2019 ◽  
Vol 8 (2S10) ◽  
pp. 873-875
Keyword(s):  
Adjacency Matrix ◽  
Singular Values ◽  
Edge Deletion ◽  
Graph Energy ◽  
Inequality Theorem

If there is an adjacency matrix A, the sum total of the singular values of A is known as the graph energy. We can find the change in energy of a graph by removing the edges using the inequality theorem on singular values. In this paper we discuss about the change in semigraph energy due to deletion of edges and its relation with distance energy

scholarly journals {0,1}-Brauer Configuration Algebras and Their Applications in Graph Energy Theory

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3042
Author(s):  
Natalia Agudelo Muñetón ◽  
Agustín Moreno Cañadas ◽  
Pedro Fernando Fernández Espinosa ◽  
Isaías David Marín Gaviria
Keyword(s):  
Adjacency Matrix ◽  
Singular Values ◽  
Great Difficulty ◽  
Trace Norm ◽  
General Finding ◽  
Graph Energy ◽  
Energy Theory ◽  
The Absolute

The energy E(G) of a graph G is the sum of the absolute values of its adjacency matrix. In contrast, the trace norm of a digraph Q, which is the sum of the singular values of the corresponding adjacency matrix, is the oriented version of the energy of a graph. It is worth pointing out that one of the main problems in this theory consists of determining appropriated bounds of these types of energies for significant classes of graphs, digraphs and matrices, provided that, in general, finding out their exact values is a problem of great difficulty. In this paper, the trace norm of a {0,1}-Brauer configuration is introduced. It is estimated and computed by associating suitable families of graphs and posets to Brauer configuration algebras.

scholarly journals Acknowledgement: edge deletion, singular values and ABC energy of graphs

2021 ◽  
Vol 87 (3) ◽  
pp. 745
Author(s):  
Modjtaba Ghorbani ◽  
Mardjan Hakimi-Nezhaad ◽  
Lihua Feng
Keyword(s):  
Singular Values ◽  
Edge Deletion

Following Estrada's method, as given in [1], Ghorbani et al. communicated in [2], and later also in [3], the following result on A-energy.

scholarly journals Graph energy change due to any single edge deletion

2015 ◽  
Vol 29 ◽  
pp. 59-73
Author(s):  
Wen-Huan Wang ◽  
Wasin So
Keyword(s):  
Partial Solution ◽  
Energy Change ◽  
Single Edge ◽  
Edge Deletion ◽  
Numerical Evidence ◽  
Graph Energy ◽  
The Absolute ◽  
Cycle Graph

The energy of a graph is the sum of the absolute values of its eigenvalues. We propose a new problem on graph energy change due to any single edge deletion. Then we survey the literature for existing partial solution of the problem, and mention a conjecture based on numerical evidence. Moreover, we prove in three different ways that the energy of a cycle graph decreases when an arbitrary edge is deleted except for the order of 4.

scholarly journals Relating graph energy with vertex-degree-based energies

2020 ◽  
Vol 68 (4) ◽  
pp. 715-725
Author(s):  
Ivan Gutman
Keyword(s):  
Adjacency Matrix ◽  
Vertex Degree ◽  
Graph Invariants ◽  
Graph Energy ◽  
The Absolute

Introduction/purpose: The paper presents numerous vertex-degree-based graph invariants considered in the literature. A matrix can be associated to each of these invariants. By means of these matrices, the respective vertex-degree-based graph energies are defined as the sum of the absolute values of the eigenvalues. Results: The article determines the conditions under which the considered graph energies are greater or smaller than the ordinary graph energy (based on the adjacency matrix). Conclusion: The results of the paper contribute to the theory of graph energies as well as to the theory of vertex-degree-based graph invariants.

A note on the relationship between graph energy and determinant of adjacency matrix

2019 ◽  
Vol 11 (01) ◽  
pp. 1950001
Author(s):  
Igor Ž. Milovanović ◽  
Emina I. Milovanović ◽  
Marjan M. Matejić ◽  
Akbar Ali
Keyword(s):  
Lower Bounds ◽  
Adjacency Matrix ◽  
Bipartite Graphs ◽  
Simple Graph ◽  
Graph Invariants ◽  
Graph Energy ◽  
The Matrix ◽  
Matrix Formula ◽  
The Relationship

Let [Formula: see text] be a simple graph of order [Formula: see text], without isolated vertices. Denote by [Formula: see text] the adjacency matrix of [Formula: see text]. Eigenvalues of the matrix [Formula: see text], [Formula: see text], form the spectrum of the graph [Formula: see text]. An important spectrum-based invariant is the graph energy, defined as [Formula: see text]. The determinant of the matrix [Formula: see text] can be calculated as [Formula: see text]. Recently, Altindag and Bozkurt [Lower bounds for the energy of (bipartite) graphs, MATCH Commun. Math. Comput. Chem. 77 (2017) 9–14] improved some well-known bounds on the graph energy. In this paper, several inequalities involving the graph invariants [Formula: see text] and [Formula: see text] are derived. Consequently, all the bounds established in the aforementioned paper are improved.

scholarly journals Graph Energies of Egocentric Networks and Their Correlation with Vertex Centrality Measures

Entropy ◽  
2018 ◽  
Vol 20 (12) ◽  
pp. 916 ◽  
Author(s):  
Mikołaj Morzy ◽  
Tomasz Kajdanowicz
Keyword(s):  
Network Models ◽  
Singular Values ◽  
Centrality Measures ◽  
Egocentric Networks ◽  
Graph Classes ◽  
Energy Distance ◽  
Graph Energy ◽  
The Matrix ◽  
Definition Of ◽  
Vertex Centrality

Graph energy is the energy of the matrix representation of the graph, where the energy of a matrix is the sum of singular values of the matrix. Depending on the definition of a matrix, one can contemplate graph energy, Randić energy, Laplacian energy, distance energy, and many others. Although theoretical properties of various graph energies have been investigated in the past in the areas of mathematics, chemistry, physics, or graph theory, these explorations have been limited to relatively small graphs representing chemical compounds or theoretical graph classes with strictly defined properties. In this paper we investigate the usefulness of the concept of graph energy in the context of large, complex networks. We show that when graph energies are applied to local egocentric networks, the values of these energies correlate strongly with vertex centrality measures. In particular, for some generative network models graph energies tend to correlate strongly with the betweenness and the eigencentrality of vertices. As the exact computation of these centrality measures is expensive and requires global processing of a network, our research opens the possibility of devising efficient algorithms for the estimation of these centrality measures based only on local information.

scholarly journals On oriented graphs with minimal skew energy

2014 ◽  
Vol 27 ◽  
Author(s):  
Shi-Cai Gong ◽  
Xueliang Li ◽  
Guanghui Xu
Keyword(s):  
Adjacency Matrix ◽  
Variable Neighborhood Search ◽  
Integral Formula ◽  
Oriented Graph ◽  
Singular Values ◽  
Neighborhood Search ◽  
External Energy ◽  
Oriented Graphs ◽  
Skew Energy ◽  
Skew Adjacency Matrix

Let S(G^σ) be the skew-adjacency matrix of an oriented graph Gσ. The skew energy of G^σ is the sum of all singular values of its skew-adjacency matrix S(G^σ). This paper first establishes an integral formula for the skew energy of an oriented graph. Then, it determines all oriented graphs with minimal skew energy among all connected oriented graphs on n vertices with m (n ≤ m < 2(n − 2)) arcs, which is analogous to the conjecture for the energy of undirected graphs proposed by Caporossi et al. [G. Caporossi, D. Cvetkovic, I. Gutman, and P. Hansen. Variable neighborhood search for extremal graphs. 2. Finding graphs with external energy. J. Chem. Inf. Comput. Sci., 39:984–996, 1999].

Energy of Graphs

2020 ◽  
pp. 267-296 ◽  
Author(s):  
Harishchandra S. Ramane
Keyword(s):  
Molecular Orbital ◽  
Electron Energy ◽  
Complete Graph ◽  
Adjacency Matrix ◽  
Close Correlation ◽  
Orbital Method ◽  
Molecular Orbital Method ◽  
Cospectral Graphs ◽  
Graph Energy ◽  
Equienergetic Graphs

The energy of a graph G is defined as the sum of the absolute values of the eigenvalues of its adjacency matrix. The graph energy has close correlation with the total pi-electron energy of molecules calculated with Huckel molecular orbital method in chemistry. A graph whose energy is greater than the energy of complete graph of same order is called hyperenergetic graph. A non-complete graph having energy equal to the energy of complete graph is called borderenergetic graph. Two non-cospectral graphs are said to be equienergetic graphs if they have same energy. In this chapter, the results on graph energy are reported. Various bounds for graph energy and its characterization are summarized. Construction of hyperenergetic, borderenergetic, and equienergetic graphs are reported.

scholarly journals Graph energy change due to edge deletion

2008 ◽  
Vol 428 (8-9) ◽  
pp. 2070-2078 ◽  
Author(s):  
Jane Day ◽  
Wasin So
Keyword(s):  
Energy Change ◽  
Edge Deletion ◽  
Graph Energy

A SVD and Modified Firefly Optimization Based Robust Digital Image Watermarking Technique

2017 ◽  
Vol 7 (7) ◽  
pp. 268
Author(s):  
Chauhan Usha ◽  
Singh Rajeev Kumar
Keyword(s):  
Digital Media ◽  
Firefly Algorithm ◽  
Image Watermarking ◽  
Singular Values ◽  
Robust Watermarking ◽  
Scaling Factors ◽  
Geometric Attacks ◽  
Host Image ◽  
Firefly Optimization ◽  
Value Decomposition

Digital Watermarking is a technology, to facilitate the authentication, copyright protection and Security of digital media. The objective of developing a robust watermarking technique is to incorporate the maximum possible robustness without compromising with the transparency. Singular Value Decomposition (SVD) using Firefly Algorithm provides this objective of an optimal robust watermarking technique. Multiple scaling factors are used to embed the watermark image into the host by multiplying these scaling factors with the Singular Values (SV) of the host image. Firefly Algorithm is used to optimize the modified host image to achieve the highest possible robustness and transparency. This approach can significantly increase the quality of watermarked image and provide more robustness to the embedded watermark against various attacks such as noise, geometric attacks, filtering attacks etc.

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