The chemical antiregular graph conjecture for total $\sigma$-irregularity

Let $G$ range over chemical graphs, and let $\sigma_t^{f(n)}$ denote the total $\sigma$-irregularity with the weight function $f(n)$. The graphs described in Theorem~

$$are the graphs under consideration. **Chemical antiregular graph conjecture.** The same graphs as in Theorem~$$

have maximum value of $\sigma_t^{f(n)}$ even if $f(n)$ is a constant in the interval $(0,1)$.

The conjecture proposes that the extremal graphs identified for the chemical-graph setting remain extremal when the weight function is any constant between $0$ and $1$, rather than only the previously considered choice. Its status is not resolved in the supplied source context.