No Huckel graph is hyperenergetic

Abstract

If G is a molecular graph with n vertices and if l1, l2, ..., ln are its eigenvalues, then the energy of G is equal to E(G) = |l1| + |l2|+ ... + |ln|. 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 p-electron energy
• energy of graph
• hyperenergetic graphs