arXiv subjects
Publications and source records attributed to Juan R. Carmona.
Let $G$ be a graph on $n$ vertices and $λ_1,λ_2,\ldots,λ_n$ its eigenvalues. The Estrada index of $G$ is an invariant that is calculated from the eigenvalues of the adjacency matrix of a graph. In this paper, we present some new lower bounds obtained for the Estrada Index of graphs and in particular of bipartite graphs that only depend on the number of vertices, the number of edges, Randić index, maximum and minimum degree and diameter.
Let $D$ be a simple digraph with eigenvalues $z_1,z_2,...,z_n$. The energy of $D$ is defined as $E(D)= \sum_{i=1}^n |Re(z_i)|$, is the real part of the eigenvalue $z_i$. In this paper a lower bound will be obtained for the spectral radius of $D$, wich improves some the lower bounds that appear in the literature \cite{G-R}, \cite{T-C}. This result allows us to obtain an upper bound for the energy of $ D $. Finally, digraphs are characterized in which this upper bound improves the bounds given in \cite{G-R} and \cite{T-C}.
Let $G$ be a graph on $n$ vertices and $λ_1,λ_2,\ldots,λ_n$ its eigenvalues. The Estrada index of $G$ is defined as $EE(G)=\sum_{i=1}^n e^{λ_i}.$ In this work, using a different demonstration technique, new lower bounds are obtained for the Estrada index, that depends on the number of vertices, the number of edges and the energy of the graph is given. Moreover, another lower bound for the Estrada index is obtained of an arbitrary non-negative Hermitian matrix are established.
Let $G$ be a graph on $n$ vertices and $λ_1\geq λ_2\geq \ldots \geq λ_n$ its eigenvalues. The Estrada index of $G$ is defined as $EE(G)=\sum_{i=1}^n e^{λ_i}.$ In this work, we using an increasing sequence converging to the $λ_1$ to obtain an increasing sequence of lower bounds for $EE(G)$. In addition, we generalize this succession for the Estrada index of an arbitrary nonnegative Hermitian matrix.