The Irregularity of a Graph

The imbalance of edge \((x,y) = | \deg(x) – \deg(y) |\).The sum of all edge imbalances in a graph is called its irregularity.
We determine the maximum irregularity of various classes of graphs.For example, the irregularity of an arbitrary graph with \(n\) vertices is less than \(\frac{4n^3}{27}\), and this bound is tight.