  The energy $E(G)$ of a graph $G$ is defined as the sum of the absolute values
of its eigenvalues. A graph $G$ of order $n$ is said to be hypoenergetic if
$E(G)<n$. Majstorovi\'{c} et al. conjectured that complete bipartite graph
$K_{2,3}$ is the only hypoenergetic connected quadrangle-containing graph with
maximum degree $\Delta \leq 3$. This paper is devoted to giving a confirmative
proof to the conjecture.
