If G is an (n,m)-graph whose spectrum consists of the numbers λ1, λ2, . . . , λn, then its Estrada index is EE(G) = ∑n i=1 e λi . We establish lower bounds for EE(G) in terms of n and m. Introduction In this paper we are concerned with simple graphs, that have no loops and no multiple or directed edges. Let G be such a graph, and let n and m be the number of its vertices and edges. Then we say ...

Large-scale time-evolving networks have been generated by many natural and technological applications, posing challenges for computation and modeling. Thus, it is of theoretical and practical significance to probe mathematical tools tailored for evolving networks. In this paper, on top of the dynamic Estrada index, we study the dynamic Laplacian Estrada index and the dynamic normalized Laplacia...

A structure-descriptor EE, recently proposed by Estrada, is examined. If λ1, λ2, . . . ,λn are the eigenvalues of the molecular graph, then EE = n ∑ i=1 eλi . In the case of benzenoid hydrocarbons with n carbon atoms and m carbon-carbon bonds, EE is found to be accurately approximated by means of the formula a1 n cosh (√ 2m/n ) +a2, where a1 ≈ 1.098 and a2 =−0.64 are empirically determined fitt...

Let G be a simple n-vertex graph whose eigenvalues are λ1, . . . , λn. The Estrada index of G is defined as EE(G) = ∑n i=1 e λi . The importance of this topological index extends much further than just pure graph theory. For example, it has been used to quantify the degree of folding of proteins and to measure centrality of complex networks. The talk aims to give an introduction to the Estrada ...

Let G be an n-vertex graph. If λ1, λ2, . . . , λn are the adjacency eigenvalues of G, then the Estrada index and the energy of G are defined as EE(G) = ∑n i=1 e λi and E(G) = ∑n i=1 |λi|, respectively. Some new lower bounds for EE(G) are obtained in terms of E(G). We also prove that if G has m edges and t triangles, then EE(G) ≥ √ n2 + 2mn+ 2nt. The new lower bounds improve previous lower bound...

The notion of strongly quotient graph (SQG) was introduced by Adiga et al. (2007). In this paper, we obtain some better results for the distance energy and the distance Estrada index of any connected strongly quotient graph (CSQG) as well as some relations between the distance Estrada index and the distance energy. We also present some bounds for the distance energy and the distance Estrada ind...

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) = Σ i=1 ei . A cactus is a connected graph in which any two cycles have at most one common vertex. In this work, the unique graph with maximal Estrada index in the class of all cacti with n vertices and k cycles was determined. Also, ...