The Second Minimum of the Irregularity of Graphs

For a graph G, Albertson [M. O. Albertson, The irregularity of a graph, Ars Comb., 46 (1997), 219-225] has defined the irregularity of G asirr(G)=∑xy∈E(G)|dG(x)−dG(y)| where dG(u) is the degree of vertex u. Recently, this graph invariant gained interest in chemical graph theory. In this work, we present some new results on the second minimum of the irregularity of graphs.