On Equienergetic, Hyperenergetic and Hypoenergetic Graphs

Samir K. Vaidya, Kalpesh M. Popat

The eigenvalue of a graph $G$ is the eigenvalue of its adjacency matrix and the energy $E(G)$ is the sum of absolute values of eigenvalues of graph $G$. Two non-isomorphic graphs $G_1$ and $G_2$ of the same order are said to be equienergetic if $E(G_1) = E(G_2)$. The graphs whose energy is greater than that of complete graph are called hyperenergetic and the graphs whose energy is less than that of its order are called hypoenergetic graphs. The natural question arises: Are there any pairs of equienergetic graphs which are also hyperenergetic (hypoenergetic)? We have found an affirmative answer of this question and contribute some new results.