Maximum ratio of (graph) irregularities

We estimate the maximum ratio between the ${\sigma }_t$- and $\sigma$-irregularity for graphs and trees of order $n$, which are respectively bounded by $\mathrm{\Theta }(n^{5\mathrm{/}2})$ and $n-2$. This answers a question and a conjecture by Filipovski et al. in an elegant way. For trees, we obtain that the (Albertson) irregularity measure $\text{irr}$ is an upper bound for the graph variance (normalised with the order).