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Estrada Index and Laplacian Estrada Index of Random Interdependent Graphs [PDF]

Mathematics, 2020
Let G be a simple graph of order n. The Estrada index and Laplacian Estrada index of G are defined by E E ( G ) = ∑ i = 1 n e λ i ( A ( G ) ) and L E E ( G ) = ∑ i = 1 n e λ i ( L ( G ) ) , where { λ i
Yilun Shang
doaj   +5 more sources

On the Harary Estrada index of graphs

Special Matrices
Let GG be a connected graph with nn vertices v1,…,vn{v}_{1},\ldots ,{v}_{n}. The Harary matrix of GG, denoted by H(G)H\left(G), is an n×nn\times n matrix with a zero main diagonal, where the (i,j)\left(i,j)-entry is 1d(vi,vj)\frac{1}{d\left({v}_{i},{v}_ ...
Oboudi Mohammad Reza
doaj   +4 more sources

Lower Bounds for Gaussian Estrada Index of Graphs [PDF]

Symmetry, 2018
Suppose that G is a graph over n vertices. G has n eigenvalues (of adjacency matrix) represented by λ1,λ2,⋯,λn. The Gaussian Estrada index, denoted by H(G) (Estrada et al., Chaos 27(2017) 023109), can be defined as H(G)=∑i=1ne-λi2. Gaussian Estrada index
YILUN Shang, Shang YILUN
exaly   +4 more sources

On the Estrada Index of Seidel Matrix [PDF]

Mathematics Interdisciplinary Research, 2020
Let G be a simple graph with n vertices and with the Seidel matrix S‎. ‎Suppose μ1‎, ‎μ2,..., μn are the Seidel eigenvalues of G‎. ‎The Estrada index of the Seidel matrix of G is defined as SEE(G)=‎∑ni=1 eμi‎.
Mardjan Hakimi-Nezhaad, Modjtaba Ghorbani   +1 more
doaj   +3 more sources

Computing the Energy and Estrada Index of Different Molecular Structures

Journal of Chemistry, 2022
Graph energy is an invariant that is derived from the spectrum of the adjacency matrix of a graph. Graph energy is actually the absolute sum of all the eigenvalues of the adjacency matrix of a graph i.e.
Zeeshan Saleem Mufti, Rukhshanda Anjum, Qin Xin, Fairouz Tchier, Iram Anwar-ul-Haq, Yaé Ulrich Gaba   +5 more
doaj   +2 more sources

On the Maximum Estrada Index of 3-Uniform Linear Hypertrees [PDF]

The Scientific World Journal, 2014
For a simple hypergraph H on n vertices, its Estrada index is defined as EE(H)=∑i=1n‍eλi, where λ1,λ2,…,λn are the eigenvalues of its adjacency matrix. In this paper, we determine the unique 3-uniform linear hypertree with the maximum Estrada index.
Faxu Li, Liang Wei, Jinde Cao, Feng Hu, Haixing Zhao   +4 more
doaj   +2 more sources

Seidel-Estrada index [PDF]

Journal of Inequalities and Applications, 2016
Let G be a simple graph with n vertices and ( 0 , 1 ) $(0,1)$ -adjacency matrix A. As usual, S ( G ) = J − 2 A − I $S(G)=J-2A-I$ denotes the Seidel matrix of the graph G. Suppose θ 1 , θ 2 , … , θ n $\theta_{1}, \theta_{2},\ldots, \theta_{n}$ and λ 1 , λ
Jalal Askari, Ali Iranmanesh, Kinkar Ch Das   +2 more
doaj   +3 more sources

Estimating the PI-Estrada index of graphs [PDF]

Discrete Mathematics Letters, 2021
Let G be a graph with n vertices. The PI-Estrada index of G is an invariant that is calculated from the eigenvalues of the vertex-PI matrix of G. The main purpose of this paper is to establish upper and lower bounds for the PI-Estrada index of a graph in
Akbar Jahanbani, Hajar Shooshtari, Jonnathan Rodriguez   +2 more
doaj   +2 more sources

Lower bounds for Estrada index and Laplacian Estrada index

Applied Mathematics Letters, 2010
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Ivan Gutman
exaly   +2 more sources

The Extremal Structures of r-Uniform Unicyclic Hypergraphs on the Signless Laplacian Estrada Index

Mathematics, 2022
SLEE has various applications in a large variety of problems. The signless Laplacian Estrada index of a hypergraph H is defined as SLEE(H)=∑i=1neλi(Q), where λ1(Q),λ2(Q),…,λn(Q) are the eigenvalues of the signless Laplacian matrix of H. In this paper, we
Hongyan Lu, Zhongxun Zhu
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