  Let $G=(V(G),E(G))$ be a simple graph with vertex set $V(G)$ and edge set
$E(G)$. Let $S$ be a subset of $V(G)$, and let $B(S)$ be the set of neighbours
of $S$ in $V(G) \setminus S$. The differential $\partial(S)$ of $S$ is defined
as $|B(S)|-|S|$. The maximum value of $\partial(S)$ taken over all subsets
$S\subseteq V$ is the differential $\partial(G)$ of $G$. A graph operator is a
mapping $F: G\rightarrow G'$, where $G$ and $G'$ are families of graphs.The
graph $\S{G}$ is defined as the graph obtained from $G$ con bipartici\'on de
v\'ertices $V(G)\cup E(G)$, donde hay tantas aristas entre $v \in V(G)$ y $e
\in E(G)$, como veces $e$ sea incidente con $v$ en $G$. In this paper we study
the relationship between $\partial(G)$ and $\partial(\S{G})$. Besides, we
relate the differential of a graph with known parameters of a graph, namely,
its domination and independence number.
