Connected Graphs With Nullity Two Are Non-Hypoenergetic

The energy of a graph g, denoted by e(g), is defined as the sum of absolute values of all eigenvaluesof g. a graph of order n, whose energy is less than n, i.e., e(g) < n, is said to be hypoenergetic. graphsfor which e(g) ≥ n are called non-hypoenergetic. a graph of order n is said to be orderenergetic, if itsenergy and its order are equal, i.e., e(g) = n. it is proved that every connected graph with nullity 2 isnon-hypoenergetic. in particular, there are only two connected orderenergetic graphs with nullity 2.