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arXiv · 1611.06959

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

Sona Pavlikova·Daniel Sevcovic
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Abstract

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. Our goal is to construct a new graph by bridging two given weighted graphs 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.

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Sona Pavlikova, Daniel Sevcovic. 2016-11-21. Maximization of the Spectral Gap for Chemical Graphs by means of a Solution to a Mixed Integer Semidefinite Program. https://arxiv.org/abs/1611.06959

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