Hyperenergetic graphs and cyclomatic number (Q2853162)

The energy of a graph is the sum of the absolute values of the eigenvalues of the adjacency matrix of the graph. A graph on \(n\) vertices is said to be hyperenergetic if its energy is greater than the energy of the complete graph on \(n\) vertices (which is equal to \(2n-2\)). It is shown that there is only a finite number of hyperenergetic graphs with a fixed cyclomatic number \(c\). In particular, there are no hyperenergetic graphs with \(c\leq8\).