Irredundant broadcast equality conjecture for graphs with no strength-one vertices

Let $G$ be a graph. A broadcast $f$ has positive-support vertices $V_f^+=\{v\in V(G):f(v)>0\}$ and strength-one vertices $V_f^1=\{v\in V(G):f(v)=1\}$. Write $\operatorname{ir}_{b}(G)$ for the minimum cost of an irredundant broadcast on $G$, and $\gamma_b(G)$ for the minimum cost of a dominating broadcast on $G$. Irredundant broadcast equality conjecture. If $G$ has an $\operatorname{ir}_{b}$-broadcast $f$ such that

$$f(v)\geq 2\quad\text{for all }v\in V_f^+,$$

then

$$\operatorname{ir}_{b}(G)=\gamma_b(G).$$

This is the second conjecture concerning the problem of characterizing graphs for which $\gamma_b=\operatorname{ir}_b$; its status is not resolved in the supplied source.