  We introduce the general Albertson irregularity index of a connected graph
$G$ and define it as $A_{p}(G) =(\sum_{uv\in
E(G)}|d(u)-d(v)|^p)^{\frac{1}{p}}$, where $p$ is a positive real number and
$d(v)$ is the degree of the vertex $v$ in $G$. The new index is not only
generalization of the well-known Albertson irregularity index and
$\sigma$-index, but also it is the Minkowski norm of the degree of vertex. We
present lower and upper bounds on the general Albertson irregularity index. In
addition, we study the extremal value on the general Albertson irregularity
index for trees of given order. Finally, we give the calculation formula of the
general Albertson index of generalized Bethe trees and Kragujevac trees.
