Abstract:
Rese a informe de investigación "etnohistoria de las caucherías del Putumayo" de Roberto Pineda Camacho / "Arqueología de rescate- proyecto carbonífero de el cerrejón -zona norte"- area de el palmar" / Arqueología de rescate- proyecto carbonífero de el cerrejon-1984 zona central - áreas de patilla y el paredón" / VASCO LUIS GUILLERMO. Jaibanás. Los Verdaderos Hombres, Biblioteca Banco Popular. Textos Universitarios, Bogotá, 1985.

Abstract:
Let $G$ be a simple graph with $n$ vertices and let $\mu_1 \geqslant \mu_2 \geqslant...\geqslant \mu_{n - 1} \geqslant \mu_n = 0$ be the eigenvalues of its Laplacian matrix. The Laplacian Estrada index of a graph $G$ is defined as $LEE (G) = \sum\limits_{i = 1}^n e^{\mu_i}$. Using the recent connection between Estrada index of a line graph and Laplacian Estrada index, we prove that the path $P_n$ has minimal, while the star $S_n$ has maximal $LEE$ among trees on $n$ vertices. In addition, we find the unique tree with the second maximal Laplacian Estrada index.

Abstract:
We first define a new Laplacian spectrum based on Estrada index, namely, Laplacian Estrada-like invariant, LEEL, and two new Estrada index-like quantities, denoted by S and , respectively, that are generalized versions of the Estrada index. After that, we obtain some lower and upper bounds for LEEL, S, and .

Abstract:
Suppose $G$ is a simple graph on $n$ vertices. The $D$-eigenvalues $\mu_1,\mu_2,\cdots,\mu_n$ of $G$ are the eigenvalues of its distance matrix. The distance Estrada index of $G$ is defined as $DEE(G)=\sum_{i=1}^ne^{\mu_i}$. In this paper, we establish new lower and upper bounds for $DEE(G)$ in terms of the Wiener index $W(G)$. We also compute the distance Estrada index for some concrete graphs including the buckminsterfullerene $C_{60}$.

Abstract:
Let $G$ be a graph with $n$ vertices and let $mu_1,mu_2,ldots,mu_n$ be its Laplacian eigenvalues. In some recent works aquantity called Laplacian Estrada index was considered, defined as$LEE(G)=sumlimits_{i=1}^n e^{mu_i}$,. We now establish somefurther properties of $LEE$, mainly upper and lower bounds interms of the number of vertices, number of edges, and the firstZagreb index.

Abstract:
We first define a new Laplacian spectrum based on Estrada index, namely, Laplacian Estrada-like invariant, LEEL, and two new Estrada index-like quantities, denoted by S and EEX, respectively, that are generalized versions of the Estrada index. After that, we obtain some lower and upper bounds for LEEL, S, and EEX.

Abstract:
The D-eigenvalues {\mu}_1,{\mu}_2,...,{\mu}_{n} of a connected graph G are the eigenvalues of its distance matrix. The distance Estrada index of G is defined in [15] as DEE=DEE(G)=\Sigma_{i=1}^n e^{{\mu}_{i}} In this paper, we give better lower bounds for the distance Estrada index of any connected graph as well as some relations between DEE(G) and the distance energy.

Abstract:
Let $G$ be a graph of order $n$. Let $lambda_{1}, lambda_{2},ldots, lambda_{n}$ be the eigenvalues of the adjacency matrix of$G$, and let $mu_{1}, mu_{2}, ldots, mu_{n}$ be the eigenvaluesof the Laplacian matrix of $G$. Much studied Estrada index of thegraph $G$ is defined as $EE=EE(G)=sumlimits^{n}_{i=1}e^{lambda_{i}}$. We define and investigate the Laplacian Estrada index of the graph $G$, $LEE=LEE(G)=sumlimits^{n}_{i=1}e^{(mu_{i}-frac{2m}{n})}$. Bounds for $LEE$ are obtained, as well as some relations between $LEE$ and graph Laplacian energy.

Abstract:
The Estrada index EE is a recently proposed molecular structure-descriptor, used in the modeling of certain features of the 3D structure of organic molecules, in particular of the degree of folding of proteins and other long-chain biopolymers. The Estrada index is computed from the spectrum of the molecular graph. Therefore, finding its relation with the spectral radius r (= the greatest graph eigenvalue) is of interest, especially because the structure-dependency of r is relatively well understood. In this work, the basic characteristics of the relation between EE and r, which turned out to be much more complicated than initially anticipated, was determined.