Consider a simple graph with a symmetric adjacency matrix. The Gaussian Estrada index is defined as the sum of exponential of the opposite number of squared adjacency eigenvalues. 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 talk, we will review this graph invariant and establish some new bounds in terms of the number of vertices, the number of edges, as well as the first Zagreb index.

Dr. Shang received the B.S. and Ph.D. degrees in mathematics from Shanghai Jiao Tong University in 2005 and 2010, respectively. His research interests include the structure and dynamics of complex networks and systems, cyber epidemic spreading, probabilistic combinatorics, and system control theory. Prior to joining Northumbria University as an associate professor, he has various appointments with Tongji University, University of Texas at San Antonio, Singapore University of Technology and Design, Hebrew University of Jerusalem, and University of Essex.
Dr. Shang has been on the Editorial Board of IEEE Access, PLoS ONE and Mathematical Biosciences and Engineering. He received the 2016 Dimitrie Pompeiu Prize from the Romanian Academy.