Gutman's non-hyperenergetic graph conjecture

Let $\Gamma$ be a finite graph, and let $K_{|v(\mathcal{G})|}$ denote the complete graph on $|v(\mathcal{G})|$ vertices. A graph is hyperenergetic if $E(\Gamma)>E(K_{|V(\Gamma)|})$. Gutman's conjecture. Any finite graph $\Gamma\ncong K_{|v(\mathcal{G})|}$ is non-hyperenergetic. The conjecture was disproved by counterexamples, so it is false in general.