Abstract: The energy $\mathcal{E}(G)$ of a graph $G$ is the sum of the absolute values of
all the eigenvalues of the adjacency matrix of $G$. It is used in chemistry to
approximate the total $\pi$-electron energy of a molecule. This paper presented some new
lower bounds for $\mathcal{E}(G)$, and characterized those graphs for which these bounds
were attained.

Key words: energy, lower bound, interlace, quotient matrix , graph, energy, lower bound, interlace, quotient matrix