A graph G is said to be orderenergetic, if its energy equal to its order and it is said to be hypoenergetic if its energy less than its order. Two non-isomorphic graphs of same order are said to be equienergetic if their energies are equal. In this paper, we construct some new families of orderenergetic graphs, hypoenergetic graphs, equienergetic graphs, equiorderenergetic graphs and equihypoenergetic graphs.