No Hückel graph is hyperenergetic

Abstract

If G is a molecular graph with n vertices and if λ1, λ2, ..., λn are its eigenvalues, then the energy of G is equal to E(G) = |λ1| + |λ2|+ ... + |λn|. If E(G) > 2n - 2, then G is said to be hyperenergetic. We show that no Hückel graph (= the graph representation of a conjugated hydrocarbon within the Hückel molecular orbital model) is hyperenergetic.

Keywords

• total π-electron energy
• energy of graph
• hyperenergetic graphs