The second-minimal total irregularity conjecture for connected graphs

Let $G$ be a simple connected graph with $n$ vertices, and let $\operatorname{irr}_{t}(G)$ denote its total irregularity. A graph is regular if all its vertices have the same degree. Second-minimal total irregularity conjecture. If $G$ is not a regular graph, then

$$\operatorname{irr}_{t}(G)\geq 2n-4.$$

The paper identifies $0$ as the minimal total irregularity, attained by regular graphs, and proposes $2n-4$ as the second-minimal value for simple connected graphs on $n$ vertices. The claim is presented as an open problem for further research.