Chapter 11, Problem 21SE

To determine

To show:

$T$ can be obtained from disjoint trees $T_0,T_1,\mathrm{.........},T_{k-1}$ with roots $r_0,r_1,r_2,\mathrm{.......},r_{k-1}$ respectively. Where $V$ is not in only of these trees where $T_i$ is a $S_i-$ tree for $i=0,1,\mathrm{.........}k-1$ by connecting $V$ to $r_0{\text{ and r}}_{i+1}$ for $i=0,1,\mathrm{........},k-1$.