Let G be a simple graph with eigenvalues λ1, λ2, . . . , λn. The Estrada index of G is defined as EE(G) = ∑ n i=1 ei . In this paper, the unique graph with maximum Estrada index is determined among connected graphs with given numbers of vertices and cut edges.

For a simple hypergraph H on n vertices, its Estrada index is defined as [Formula in text], where λ 1, λ 2,…, λ n are the eigenvalues of its adjacency matrix. In this paper, we determine the unique 3-uniform linear hypertree with the maximum Estrada index.

Let G be a simple graph with eigenvalues λ1, λ2, . . . , λn. The Estrada index of G is defined as EE(G) = ∑ n i=1 ei . In this paper, the unique graph with maximum Estrada index is determined among connected graphs with given numbers of vertices and cut edges.

Several hundreds of so-called molecular structuredescriptors were proposed in the chemical literature [1] and are used for modeling of various physical and chemical properties of (mainly) organicmolecules. In general, a molecular structure-descriptor is a number, usually computed from the molecular graph [2, 3], that reflects certain topological features [4, 5] of the underlying molecule. Many ...

Let λ1, λ2, · · · , λn be the eigenvalues of the distance matrix of a connected graph G. The distance Estrada index of G is defined as DEE(G) = ∑ n i=1 ei . In this note, we present new lower and upper bounds for DEE(G). In addition, a Nordhaus-Gaddum type inequality for DEE(G) is given. MSC 2010: 05C12, 15A42.

The Estrada index was used to study the folding degree of proteins and other long-chain molecules [4, 5, 6, 9]. It also has numerous applications in the vast field of complex networks [7, 8, 13, 14, 17]. A number of properties especially lower and upper bounds [3, 10, 11, 12, 15, 16, 18, 19, 20] for the Estrada index are known. In this paper, we establish further lower bounds improving some res...

Let G be a simple connected graph on n vertices and λ1, λ2, . . . , λn be the eigenvalues of the adjacency matrix of G. The Estrada index of G is defined as EE(G) = n i=1 e λi . LetTn be the class of tricyclic graphs G on n vertices. In this paper, the graphs inTn with themaximal Estrada index is characterized. © 2013 Elsevier B.V. All rights reserved.

Let G be a simple graph of order n with eigenvalues λ1, λ2, · · · , λn and normalized Laplacian eigenvalues μ1,μ2, · · · ,μn. The Estrada index and normalized Laplacian Estrada index are defined as EE(G) = ∑n k=1 e λk and LEE(G) = ∑n k=1 e μk−1, respectively. We establish upper and lower bounds to EE and LEE for edge-independent random graphs, containing the classical Erdös-Rényi graphs as spec...

The logarithm of the Estrada index has been recently proposed as a spectral measure to characterize the robustness of complex networks. We derive novel analytic lower bounds for the logarithm of the Estrada index based on the Laplacian spectrum and the mixing times of random walks on the network. The main techniques employed are some inequalities, such as the thermodynamic inequality in statist...