Abstract
The irregularity of a graph is the sum of the absolute values of the differences of degrees of pairs of adjacent vertices. The extremal graph with minimal irregularity among trees of order \(n\) with maximum degree \(\Delta\) and the second maximum degree
\(\Delta_1\) are determined, as well as unicyclic graphs of order \(n\) with girth \(g\) and maximum degree \(\Delta\). Lower and upper bounds are established on irregularity. Furthermore, the inverse problem for the irregularity of maximally
irregular graphs is solved.
