  Gutman and Wagner proposed the concept of matching energy (ME) and pointed
out that the chemical applications of ME go back to the 1970s. Let $G$ be a
simple graph of order $n$ and $\mu_1,\mu_2,\ldots,\mu_n$ be the roots of its
matching polynomial. The matching energy of $G$ is defined to be the sum of the
absolute values of $\mu_{i}\ (i=1,2,\ldots,n)$. In this paper, we characterize
the graphs with minimal matching energy among all unicyclic and bicyclic graphs
with a given diameter $d$.
