Abstract
The energy of a graph \(G\), denoted by \(\mathcal{E}(G)\), is defined as the sum of absolute values of all eigenvalues of \(G\). A graph of order \(n\), whose energy is less than \(n\), i.e., \(\mathcal{E}(G) < n\), is said to be hypoenergetic. Graphs for which \(\mathcal{E}(G) \geq n\) are called non-hypoenergetic. A graph of order \(n\) is said to be orderenergetic, if its energy and its order are equal, i.e., \(\mathcal{E}(G) = n\). In this paper, we characterize non-hypoenergetic graphs with nullity 2. It is proved that except two graphs, every connected graph with nullity 2 is non-hypoenergetic.