2 problems

Let $n\geq 5$. For even $n$, let $S_{(n-2)/2}\mathbin{\cdot}S_{(n-2)/2}$ denote the merged star formed from two stars of parameter $(n-2)/2$; for odd $n$, let…

Let $n\geq 5$ and let $S_{n-1}$ denote the star on $n-1$ vertices. For a tree $T$, write $\mathrm{uB}(T)$ for its distance-unbalancedness index. Minimum distance-unbalancedness con…