  For a graph $G$ the imbalance of an edge $uv$ of $G$ is
$|deg_G(u)-deg_G(v)|$. Irregularity of a graph $G$ is defined as the sum of
imbalances over all edges of $G$. In this paper we consider expansions and Pell
graphs. If $H$ is an expansion of $G$ with respect to the sets $V_1$ and $V_2$,
we express the irregularity of $H$ using $G, V_1$ and $V_2$. For Pell graphs
the imbalance of their edges is studied. The number of edges of a Pell graph
with a fixed imbalance $k$ is expressed. Using these results the irregularity
and the $\sigma$-index of Pell graphs are given.
