Maximization of the Spectral Gap for Chemical Graphs by means of a Solution to a Mixed Integer Semidefinite Program
Optimization and Control
2016-11-22 v1
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.
Keywords
Cite
@article{arxiv.1611.06959,
title = {Maximization of the Spectral Gap for Chemical Graphs by means of a Solution to a Mixed Integer Semidefinite Program},
author = {Sona Pavlikova and Daniel Sevcovic},
journal= {arXiv preprint arXiv:1611.06959},
year = {2016}
}