Hyperenergetic and Hypoenergetic Graphs

Ivan Gutman

The energy $E=E(G)$ of a graph $G$ is the sum of the absolute values of the eigenvalues of $G$. The motivation for the introduction of this invariant comes from chemistry, where results on $E$ were obtained already in the 1940's. A graph $G$ with $n$ vertices is said to be ``hyperenergetic'' if $E>2n-2$, and to be ``hypoenergetic'' if $E(G)