Hypoenergetic molecular graphs

Abstract

The energy E of a (molecular) graph is equal to the sum of the absolute values of its eigenvalues. A molecular graph is said to be hypoenergetic if E<n, where n is the number of vertices. There are only four hypoenergetic graphs with maximal vertex degree not exceeding 3, i.e. graphs representing conjugated π-electron systems. However, there are infinitely many hypoenergetic graphs with maximal vertex degree equal to 4, i.e. molecular graphs of saturated hydrocarbons.