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Symmetry 2018, 10(8), 325;

Lower Bounds for Gaussian Estrada Index of Graphs

School of Mathematical Sciences, Tongji University, Shanghai 200092, China
Received: 3 July 2018 / Revised: 3 August 2018 / Accepted: 6 August 2018 / Published: 7 August 2018
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Suppose that G is a graph over n vertices. G has n eigenvalues (of adjacency matrix) represented by λ1,λ2,,λn. The Gaussian Estrada index, denoted by H(G) (Estrada et al., Chaos 27(2017) 023109), can be defined as H(G)=i=1neλi2. Gaussian Estrada index underlines the eigenvalues close to zero, which plays an important role in chemistry reactions, such as molecular stability and molecular magnetic properties. In a network of particles governed by quantum mechanics, this graph-theoretic index is known to account for the information encoded in the eigenvalues of the Hamiltonian near zero by folding the graph spectrum. In this paper, we establish some new lower bounds for H(G) in terms of the number of vertices, the number of edges, as well as the first Zagreb index. View Full-Text
Keywords: Gaussian Estrada index; Zagreb index; lower bound; graph spectrum Gaussian Estrada index; Zagreb index; lower bound; graph spectrum
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Shang, Y. Lower Bounds for Gaussian Estrada Index of Graphs. Symmetry 2018, 10, 325.

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