Irregularity of Graphs

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 ∆ and the second maximum degree ∆1 are determined, as well as unicyclic graphs of order n with girth g and maximum degree ∆. Lower and upper bounds are established on irregularity. Furthermore, the inverse problem for the irregularity of maximally irregular graphs is solved.