  An $(a,b)$-biregular bipartite graph is a bipartite graph with bipartition
$(X, Y)$ such that each vertex in $X$ has degree $a$ and each vertex in $Y$ has
degree $b$. By the bipartite expander mixing lemma, biregular bipartite graphs
have nice pseudorandom and expansion properties when the second largest
adjacency eigenvalue is not large. In this paper, we prove several explicit
properties of biregular bipartite graphs from spectral perspectives. In
particular, we show that for any $(a,b)$-biregular bipartite graph $G$, if the
spectral gap is greater than $\frac{2(k-1)}{\sqrt{(a+1)(b+1)}}$, then $G$ is
$k$-edge-connected; and if the spectral gap is at least
$\frac{2k}{\sqrt{(a+1)(b+1)}}$, then $G$ has at least $k$ edge-disjoint
spanning trees. We also prove that if the spectral gap is at least
$\frac{(k-1)\max\{a,b\}}{2\sqrt{ab - (k-1)\max\{a,b\}}}$, then $G$ is
$k$-connected for $k\ge 2$; and if the spectral gap is at least
$\frac{6k+2\max\{a,b\}}{\sqrt{(a-1)(b-1)}}$, then $G$ has at least $k$
edge-disjoint spanning 2-connected subgraphs. We have stronger results in the
paper.
