Extremely Irregular Unicyclic Graphs

R. Nasiri, A. Gholami, G. H. Fath-Tabar, H. R. Ellahi

The irregularity of a graph is defined to be the sum of absolute values of the differences of the degrees of endpoints of each edge. In this paper, we present some new results on the irregularity of unicyclic graphs, and then characterize all unicyclic graphs on $n$ vertices with irregularity values greater than or equal to $n^2-9n+24$.