Maximization of the Spectral Gap for Chemical Graphs by means of a Solution to a Mixed Integer Semidefinite Program

Maximization of the Spectral Gap for Chemical Graphs by means of a Solution to a Mixed Integer Semidefinite Program

Soňa  Pavlíková, Daniel Ševčovič

FCFT, Slovak University of Technology, 812 37 Bratislava, Slovakia, and FMFI, Comenius University, 842 48 Bratislava, Slovakia.



In this paper we analyze the spectral gap of a weighted graph which is the difference between the smallest positive and largest negative eigenvalue of its adjacency matrix. Such a graph can represent e.g. a chemical organic molecule. Given two weighted graphs, our goal is to construct a new graph by bridging them over a bipartite graph.  The aim is to maximize the spectral gap with respect to a bridging graph. To this end, we construct a mixed integer semidefinite program for maximization of the spectral gap and compute it numerically.

Cite as:

Pavlíková, S., Ševčovič, D. (2016). Maximization of the Spectral Gap for Chemical Graphs by means of a Solution to a Mixed Integer Semidefinite Program. Computer Methods in Materials Science, 16(4), 169 – 176.

Article (PDF):


Chemical molecular graphs, Invertible graph, HOMO-LUMO spectral gap, Bridged graph, Schur complement, Mixed integer semidefinite programming


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