The extremal irregularity of connected graphs with given number of pendant vertices

The irregularity of a graph G = ( V, E ) is defined as the sum of imbalances ∣ d u − d v ∣ over all edges uv ∈ E , where d u denotes the degree of the vertex u in G . This graph invariant, introduced by Albertson in 1997, is a measure of the defect of regularity of a graph. In this paper, we completely determine the extremal values of the irregularity of connected graphs with n vertices and p pendant vertices (1 ⩽ p ⩽ n − 1), and characterize the corresponding extremal graphs.