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. 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.