  Let $\mathcal{G} = (\mathcal{V}, \mathcal{E})$ be a simple graph, an
$L(2,1)$-labeling of $\mathcal{G}$ is an assignment of labels from nonnegative
integers to vertices of $\mathcal{G}$ such that adjacent vertices get labels
which differ by at least by two, and vertices which are at distance two from
each other get different labels. The $\lambda$-number of $\mathcal{G}$, denoted
by $\lambda(\mathcal{G})$, is the smallest positive integer $\ell$ such that
$\mathcal{G}$ has an $L(2,1)$-labeling with all labels as members of the set
$\{0,1, \dots,\ell\}$. The zero-divisor graph of a finite commutative ring $R$
with unity, denoted by $\Gamma(R)$, is the simple graph whose vertices are all
zero divisors of $R$ in which two vertices $u$ and $v$ are adjacent if and only
if $uv = 0$ in $R$. In this paper, we investigate $L(2,1)$-labeling of some
zero-divisor graphs. We study the partite truncation, a graph operation that
allows us to obtain a reduced graph of relatively small order from a graph of
significantly larger order. We establish the relation between $\lambda$-numbers
of the graph and its partite truncated one. We make use of the operation
partite truncation to contract the zero-divisor graph of a reduced ring to the
zero-divisor graph of a Boolean ring.
