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 Eccentricity energy change of complete multipartite graphs due to edge deletion

2022 ◽  
Vol 10 (1) ◽  
pp. 193-202
Author(s):  
Iswar Mahato ◽  
M. Rajesh Kannan
Keyword(s):  
Distance Matrix ◽  
Energy Change ◽  
Energy Increase ◽  
Edge Deletion ◽  
Multipartite Graphs ◽  
Complete Multipartite Graphs ◽  
Distance Matrices ◽  
The Absolute ◽  
Complete Multipartite

Abstract The eccentricity matrix ɛ(G) of a graph G is obtained from the distance matrix of G by retaining the largest distances in each row and each column, and leaving zeros in the remaining ones. The eccentricity energy of G is sum of the absolute values of the eigenvalues of ɛ(G). Although the eccentricity matrices of graphs are closely related to the distance matrices of graphs, a number of properties of eccentricity matrices are substantially different from those of the distance matrices. The change in eccentricity energy of a graph due to an edge deletion is one such property. In this article, we give examples of graphs for which the eccentricity energy increase (resp., decrease) but the distance energy decrease (resp., increase) due to an edge deletion. Also, we prove that the eccentricity energy of the complete k-partite graph Kn 1, ... , nk with k ≥ 2 and ni ≥ 2, increases due to an edge deletion.

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

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.

On Statistics of Graph Energy

2001 ◽  
Vol 56 (3-4) ◽  
pp. 307-311 ◽  
Author(s):  
Ante Graovac ◽  
Ivan Gutman ◽  
Peter E. John ◽  
Dušica Vidović ◽  
Ivana Vlah
Keyword(s):  
Electron Energy ◽  
Molecular Graph ◽  
Molecular Graphs ◽  
Average Value ◽  
Graph Energy ◽  
The Absolute ◽  
The Difference ◽  
Conjugated Molecule

Abstract The energy EG of a graph G is the sum of the absolute values of the eigenvalues of G. In the case whene G is a molecular graph, EG is closely related to the total π-electron energy of the corresponding conjugated molecule. We determine the average value of the difference between the energy of two graphs, randomly chosen from the set of all graphs with n vertices and m edges. This result provides a criterion for deciding when two (molecular) graphs are almost coeneigetic.

scholarly journals On the Change of Distance Energy of Complete Bipartite Graph due to Edge Deletion

2021 ◽  
Vol 2021 ◽  
pp. 1-3
Author(s):  
Shaowei Sun ◽  
Ziyan Wan
Keyword(s):  
Bipartite Graph ◽  
Complete Bipartite Graph ◽  
Quadratic Polynomial ◽  
Edge Deletion ◽  
Cubic Polynomial ◽  
The Absolute

The distance energy of a graph is defined as the sum of absolute values of distance eigenvalues of the graph. The distance energy of a graph plays an important role in many fields. By constructing a new polynomial, we transform a problem on the sum of the absolute values of the roots of a quadratic polynomial into a problem on the largest root of a cubic polynomial. Hence, we give a new and shorter proof on the change of distance energy of a complete bipartite graph due to edge deletion, which was given by Varghese et al.

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.

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].

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