图的预解Estrada指标的界的估计（英文）

n阶图G的子图中心度,即后来著名的Estrada指标定义为EE（G）=∑_（i=1）~N e~（λ2）.其中λ_1,λ_2……λ_n为图G的特征值.作为复杂网络的一种中心性测度和一种分子结构描述符,Estrada指标在许多研究领域有着广泛的应用.最近,Estrada和High-ama引进了一种新的复杂网络中心度,即∑_（i=1）~n n-1n-1λ_i：他们称之为预解中心度,后来又被称为预解Estrada指标.本文主要利用图G的顶点数和边数给出了图G的预解Estrada指标的若干界.     

双圈图的最大Estrada指数

令Bn^＋表示顶点个数为礼的双圈二部图的集合．考虑了召吉中图依Estrada指数从大到小的排序问题．利用二部图的Estrada指数和最大特征值之间的关系,当n≥8时,得到了Bn^＋中具有最大和次大Estrada指数的图．     

循环图的预解Estrada指标

Circulant graphs are an important class of network topology. Let G be a simple graph with n vertices, let A be the adjacency matrix of G, and λ₁,λ₂,…,λ_n be the eigenvalues of graph G. As a kind of centrality of complex networks, the resolvent Estrada index of G is defined as EE_r(G)=((1-λ_i)/(n-1))^-1. By Ramanujan's sum, using the Euler function and Mobius function, we characterize the lower bound of resolvent Estrada index of circulant graph, and obtain some computational formulas of integral circulant graphs.     

Smooth function topological structure descriptors based on graph-spectra

The spectral topological indices: energy and Estrada index of a graph are generalized for any smooth function. The smooth function indices are introduced for this purpose as well as, via positive definite square summable functions, the Shannon entropy of a graph. Some comparative values are given between linear chains and cycles.     

Correlation between the Estrada index and π-electronic energies for benzenoid hydrocarbons with applications to boron nanotubes

In this article, we present an efficient computer-based computational technique to compute the energy and Estrada index of graphs. It is shown that our computational method is more efficient and bears less computational and algorithmic complexity. We use our method to show the main result of this article, which asserts that the Estrada index correlates with the π-electronic energies of lower benzenoid hydrocarbons with correlation coefficient 0.9993. This enhances the practical applicability of the Estrada index and warrants its further usage in quantitative structure activity relationships. We further apply our computational technique in computing the energy and Estrada index of two infinite families of boron triangular nanotubes. We perform simulation based on certain computer software packages to study the graph-theoretic behavior of the obtained results. Our results help to correlate certain physicochemical properties of underlying chemical structures of these nanotubes.     

图的广义Randi\'{c} Estrada 指标的界

受图的Randi\'{c} Estrada 指标和广义 Randi\'{c} 能量的启发, 定义了图的广义 Randi\'{c} Estrada 指标. 利用代数方法和初等分析方法给出了n 阶简 单连通图和 r-正则图的广义Randi\'{c} Estrada指标的上下界, 推广了Bozkurt等人有关Randi\'{c} Estrada指标的结论.     

Bounds of the Estrada index of graphs

Let G be a graph of order n and let λ1,λ2,...,λn be its eigenvalues. The Estrada index[2] of G is defined as EE = EE(G) =∑n i=1 eλi. In this paper, new bounds for EE are established, as well as some relations between EE and graph energy E.