New Lower Bounds for Estrada Index

Some Lower Bounds for Estrada Index

Albertson energy and Albertson Estrada index of graphs

‎Let $G$ be a graph of order $n$ with vertices labeled as $v_1‎, ‎v_2,dots‎ , ‎v_n$‎. ‎Let $d_i$ be the degree of the vertex $v_i$ for $i = 1‎, ‎2‎, ‎cdots‎ , ‎n$‎. ‎The Albertson matrix of $G$ is the square matrix of order $n$ whose $(i‎, ‎j)$-entry is equal to $|d_i‎ - ‎d_j|$ if $v_i $ is adjacent to $v_j$ and zero‎, ‎otherwise‎. ‎The main purposes of this paper is to introduce the Albertson ...

Ela Lower Bounds for the Estrada Index of Graphs

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...

Bounds of distance Estrada index of graphs

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.

Lower Bounds for the Estrada Index Using Mixing Time and Laplacian Spectrum

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...