The Minimal Total Irregularity of Some Classes of Graphs

In [1], Abdo and Dimitov defined the total irregularity of a graph G = (V, E) as irr t ( G ) = 1 2 ∑ u , v ∈ V | d G ( u ) − d G ( v ) | , where dG(u) denotes the vertex degree of a vertex u ∈ V. In this paper, we investigate the minimal total irregularity of the connected graphs, determine the minimal, the second minimal, the third minimal total irregularity of trees, unicyclic graphs, bicyclic graphs on n vertices, and propose an open problem for further research.