Some Bounds on the Seidel Energy of Graphs (original) (raw)

Some Lower Bounds for Laplacian Energy of Graphs

2009

The Laplacian energy of a graph G is defined as LE(G )= n=1 |λi − 2m n |, where λ1(G) ≥ λ2(G), ..., ≥ λn(G) = 0 are the Laplacian eigenvalues of the graph G. Some lower bounds for Laplacian energy of graphs are presented in this note.

On energy and Laplacian energy of graphs

Let G = (V, E) be a simple graph of order n with m edges. The energy of a graph G, denoted by E(G), is defined as the sum of the absolute values of all eigenvalues of G. The Laplacian energy of the graph G is defined as

Milovanović Bounds for Seidel Energy of a Graph

2016

In this paper Seidel Energy of Cocktail Party graph and Crown graph are computed. Recently Milovanović et al. gave a sharper lower bounds for energy of a graph. Similar bounds for Siedel energy of a graph are established. AMS Subject Classification: Primary 05C50, 05C69.

On New Bounds for Energy of Graphs

Advances in Mathematics: Scientific Journal, 2020

The term energy was first coined by I. Gutman in chemistry, while finding the total π−electron energy of conjugated carbon compounds. In 1971 McClelland obtained both lower and upper bounds for π−electron energy. In this paper we established new bounds for energy of graphs and it also contains bounds for the largest eigenvalue and the absolute smallest eigenvalue.

A Note on Normalized Laplacian Energy of Graphs

The main goal of this paper is to obtain some bounds for the normalized Laplacian energy of a connected graph. The normalized Laplacian energy of the line and para-line graphs of a graph are investigated. The relationship of the smallest and largest positive normalized Laplacian eigenvalues of graphs are also studied.

New Bounds on the Energy of a Graph

2021

The energy of a graph G, denoted by E(G), is defined as the sum of the absolute values of all eigenvalues of G. In this paper, lower and upper bounds for energy in some of the graphs are established, in terms of graph invariants such as the number of vertices, the number of edges, and the number of closed walks.

Energy and Laplacian energy of graphs

Let G be a graph with n vertices and m edges. Let λ 1 ≥ λ 2 ≥ · · · ≥ λ n−1 ≥ λ n denote the eigenvalues of adjacency matrix A(G) of graph G . respectively. Then the Laplacian energy and the signless Laplacian energy of G are defined as

Upper Bounds for the Energy of Graphs

2013

The energy of a graph G, denoted by E(G), is defined as the sum of the absolute values of all eigenvalues of G . In this paper we present some new upper bounds for E(G) in terms of number of vertices, number of edges, clique number, minimum degree, and the first Zagreb index.

More on the relation between energy and Laplacian energy of graphs

… in Mathematical and in …, 2009

I. Gutman et al. have recently conjectured that the energy of a graph does not exceed its Laplacian energy. We disprove this conjecture by giving a few small counterexamples and, in addition, an infinite set of counterexamples. Nevertheless, we do show that the standard ...

On the Laplacian eigenvalues of a graph and Laplacian energy

Linear Algebra and its Applications, 2015

Let G be a simple graph with n vertices, m edges, maximum degree Δ, average degree d = 2m n , clique number ω having Laplacian eigenvalues μ 1 , μ 2 ,. .. , μ n−1 , μ n = 0. For k (1 ≤ k ≤ n), let S k (G) = k i=1 μ i and let σ (1 ≤ σ ≤ n − 1) be the number of Laplacian eigenvalues greater than or equal to average degree d. In this paper, we obtain a lower bound for S ω−1 (G) and an upper bound for S σ (G) in terms of m, Δ, σ and clique number ω of the graph. As an application, we obtain the stronger bounds for the Laplacian energy LE(G) = n i=1 |μ i − d|, which improve some well known earlier bounds.

Energy of Nonsingular Graphs: Improving Lower Bounds

Journal of Mathematics

Let G be a simple graph of order n and A be its adjacency matrix. Let λ 1 ≥ λ 2 ≥ … ≥ λ n be eigenvalues of matrix A . Then, the energy of a graph G is defined as ε G = ∑ i = 1 n λ i . In this paper, we will discuss the new lower bounds for the energy of nonsingular graphs in terms of degree sequence, 2-sequence, the first Zagreb index, and chromatic number. Moreover, we improve some previous well-known bounds for connected nonsingular graphs.

On the bounds for signless Laplacian energy of a graph

Discrete Applied Mathematics, 2017

For a simple graph G with n-vertices, m edges and having signless Laplacian eigenvalues q 1 , q 2 ,. .. , q n , the signless Laplacian energy QE(G) of the graph G is defined as QE(G) =  n i=1 | q i − d |, where d = 2m n is the average degree of G. In this paper, we obtain the lower and upper bounds for the signless Laplacian energy QE(G) in terms of clique number ω, maximum degree ∆, number of vertices n, first Zagreb index M 1 (G) and number of edges m. As an application, we obtain the bounds for the energy of line graph L (G) of a graph G in terms of various graph parameters. We also obtain a relation between the signless Laplacian energy QE(G) and the incidence energy IE(G).

New upper bounds for the energy and signless Laplacian energy of a graph

International Journal of Advances in Applied Mathematics and Mechanics, 2015

Let M = (m i j) be an n × n real symmetric matrix with eigenvalues µ 1 (M) ≥ µ 2 (M) ≥ ... ≥ µ n (M). The energy Eng (M) and spread Spr (M) of M are defined respectively as n i =1 |µ i (M) − Tr a(M) n | and µ 1 (M) − µ n (M), where Tr a(M) := n i =1 µ i (M) is the trace of M. In this note we first present an inequality on the energy and spread of M. Then we obtained new upper bounds for the energy and signless Laplacian energy of a graph by applying that inequality to the adjacency matrix and signless Laplacian matrix of a graph.

Some remarks on Laplacian eigenvalues and Laplacian energy of graphs

2010

Sažetak Suppose mu1\ mu_1 mu1, mu2\ mu_2 mu2,..., mun\ mu_n mun are Laplacian eigenvalues of a graph $ G .TheLaplacianenergyof. The Laplacian energy of .TheLaplacianenergyof G $ is defined as $ LE (G)=\ sum_ {i= 1}^ n|\ mu_i-2m/n| .Inthispaper,somenewboundsfortheLaplacianeigenvaluesandLaplacianenergyofsomespecialtypesofthesubgraphsof. In this paper, some new bounds for the Laplacian eigenvalues and Laplacian energy of some special types of the subgraphs of .Inthispaper,somenewboundsfortheLaplacianeigenvaluesandLaplacianenergyofsomespecialtypesofthesubgraphsof K_n $ are presented.

A lower bound for the energy of hypoenergetic and non hypoenergetic graphs

Match-communications in Mathematical and in Computer Chemistry, 2020

Let G be a simple undirected graph with n vertices and m edges. The energy of G, E(G) corresponds to the sum of its singular values. This work obtains lower bounds for E(G) where one of them generalizes a lower bound obtained by Mc Clelland in 1971 to the case of graphs with given nullity. An extension to the bipartite case is given and, in this case, it is shown that the lower bound 2 √ m is improved. The equality cases are characterized. Moreover, a simple lower bound that considers the number of edges and the diameter of G is derived. A simple lower bound, which improves the lower bound 2 √ n− 1, for the energy of trees with n vertices and diameter d is also obtained. 1 Notation and Preliminaries In this work we deal with an (n,m)-graph G which is an undirected simple graph with vertex set V (G) and edge set E (G) of cardinality n and m, respectively. As usual we denote the adjacency matrix of G by A = A(G). The eigenvalues of G are the eigenvalues of A (see e.g. [5, 6]). Its eig...

Bounds for various graph energies

ITM Web of Conferences

In this paper, we obtain some upper and lower bounds for the spectral radius of some special matrices such as maximum degree, minimum degree, Randic, sum-connectivity, degree sum, degree square sum, first Zagreb and second Zagreb matrices of a simple connected graph G by the help of matrix theory. We also get some upper bounds for the corresponding energies of G.