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arXiv · 1806.00870

On Construction of Upper and Lower Bounds for the HOMO-LUMO Spectral Gap

Sona Pavlikova·Daniel Sevcovic
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Abstract

In this paper we study spectral properties of graphs which are constructed from two given invertible graphs by bridging them over a bipartite graph. We analyze the so-called HOMO-LUMO spectral gap which is the difference between the smallest positive and largest negative eigenvalue of the adjacency matrix of a graph. We investigate its dependence on the bridging bipartite graph and we construct a mixed integer semidefinite program for maximization of the HOMO-LUMO gap with respect to the bridging bipartite graph. We also derive upper and lower bounds for the optimal HOMO-LUMO spectral graph by means of semidefinite relaxation techniques. Several computational examples are also presented in this paper.

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Sona Pavlikova, Daniel Sevcovic. 2018-06-03. On Construction of Upper and Lower Bounds for the HOMO-LUMO Spectral Gap. https://doi.org/10.3934/naco.2019005

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