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 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 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.

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 The dielectric coefficients of gases.— Part I. The rare gases and hydrogen

1931 ◽  
Vol 132 (820) ◽  
pp. 569-585 ◽  
Keyword(s):  
Great Difficulty ◽  
Relative Accuracy ◽  
Rare Gases ◽  
Electric Moment ◽  
Different Temperatures ◽  
The Absolute

The heterodyne beat method affords a means of measuring the dielectric coefficients of gases with a relative accuracy exceeding that of any of the older determinations, and in consequence it has been employed by a number of observers during recent years. The published results, however, in many cases, refer mainly to the method, and measurements are restricted to one or two gases apparently selected at random. Such determinations when made at different temperatures suffice to determine the electric moment, but owing to the great difficulty of measuring the absolute values, the figures for the dielectric coefficients themselves obtained by different observers cannot be co-ordinated.

scholarly journals Some New Results on Various Graph Energies of the Splitting Graph

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Zheng-Qing Chu ◽  
Saima Nazeer ◽  
Tariq Javed Zia ◽  
Imran Ahmed ◽  
Sana Shahid
Keyword(s):  
Adjacency Matrix ◽  
Connected Graph ◽  
Absolute Value ◽  
Regular Splitting ◽  
The Absolute ◽  
Splitting Graph ◽  
Simple Connected Graph

The energy of a simple connected graph G is equal to the sum of the absolute value of eigenvalues of the graph G where the eigenvalue of a graph G is the eigenvalue of its adjacency matrix AG. Ultimately, scores of various graph energies have been originated. It has been shown in this paper that the different graph energies of the regular splitting graph S′G is a multiple of corresponding energy of a given graph G.

scholarly journals VIII. The Bakerian Lecture.—Experimental of laws of magneto-electric induction in different masses of the same metal, and of Intensity in different metals

1833 ◽  
Vol 123 ◽  
pp. 95-142 ◽  
Keyword(s):  
Great Difficulty ◽  
The Other ◽  
Present Purpose ◽  
Electric Induction ◽  
Other Substances ◽  
The Subject ◽  
The Absolute ◽  
Experimental Researches

Mr. Faraday's highly interesting papers, entitled “Experimental Researches in Electricity,” having been referred to me, to report on, by the President and Council of this Society, I necessarily entered minutely into all the experiments and conclusions of the author, and the more so that I had had the advantage of witnessing many of the most important of these experiments. It is foreign to my present purpose to descant upon the value of Mr. Faraday’s discovery, or the merits of his communication ; the President and Council have marked their opinion of these by the award of the Copley Medal: but I may be permitted to state, that no one can concur more cordially than I do in the propriety of that award. Agreeing as I did generally with the author, both in the views which he took of the subject, and in the conclusions which he drew from his experiments, there was one, however, which I felt great difficulty in adopting, viz. “That when metals of different kinds are equally subject, in every circumstance, to magneto-electric induction, they exhibit exactly equal powers with respect to the currents which either are formed, or tend to form, in them :" and that “the same is probably the case in all other substances.” Although the experiments might appear to indicate that this was possibly the case, I did not consider them to be conclusive. The most conclusive experiment, that of two spirals, one of copper and the other of iron, transmitting opposite currents, was quite consistent with the absolute equality of the currents excited in copper and iron; but, at the same time, the apparent equality of the currents might be due to their inequality being counteracted by a corresponding inequality in the facility of transmission.

On the energy and Estrada index of Cayley graphs

2015 ◽  
Vol 07 (01) ◽  
pp. 1550005 ◽  
Author(s):  
Modjtaba Ghorbani
Keyword(s):  
Adjacency Matrix ◽  
Cayley Graphs ◽  
Estrada Index ◽  
The Absolute

The concept of energy of a graph was first defined in 1978 by Gutman as the sum of the absolute values of the eigenvalues of its adjacency matrix. Let λ1, λ2, …, λn be eigenvalues of graph Γ, then the Estrada index of Γ is defined as [Formula: see text]. The aim of this paper is to estimate the energy and Estrada index of Cayley graphs Cay (G, S) where G ≅ D2n, U6n and S is a normal symmetric generating subset of G.

scholarly journals On the Seidel Energy of Certain Mesh Derived Networks

2019 ◽  
Vol 9 (2) ◽  
pp. 1905-1910
Keyword(s):  
Adjacency Matrix ◽  
Seidel Matrix ◽  
Energy Of Graph ◽  
The Absolute ◽  
Manual Calculation

The energy of graph G is defined as the sum of the absolute values of eigenvalues of the adjacency matrix A(G). The manual calculation of energy of graphs consumes several man hours. In this paper, we use MATLAB to generate the Seidel matrix and hence calculate the Seidel energy of some mesh derived networks.

scholarly journals A Note on Skew Energy of Hadamard Graph

2019 ◽  
Vol 9 (1S4) ◽  
pp. 1010-1013
Keyword(s):  
Adjacency Matrix ◽  
Oriented Graph ◽  
Eigen Values ◽  
Skew Energy ◽  
The Absolute

The skew spectrum and skew energy of an oriented graph are respectively the set of eigenvalues of the adjacency matrix of and the sum of the absolute values of the eigen values of the adjacency matrix of . In this work, we find and study the skew spectrum and the skew energy of Hadamard graph for a particular orientation.

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.

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