A k -ended tree is a with at most leaves. In this note, we give simple proof for the following theorem. Let G be connected graph and an integer ( ≥ 2 ). S vertex subset of such that α ) ≤ + κ − 1 . Then, has which covers Moreover, condition sharp.

An independent broadcast on a connected graph $G$is a function $f:V(G)to mathbb{N}_0$such that, for every vertex $x$ of $G$, the value $f(x)$ is at most the eccentricity of $x$ in $G$,and $f(x)>0$ implies that $f(y)=0$ for every vertex $y$ of $G$ within distance at most $f(x)$ from $x$.The broadcast independence number $alpha_b(G)$ of $G$is the largest weight $sumlimits_{xin V(G)}f(x)$of an ind...