Graffiti's radius lower bound for the independence number

Let $G$ be a graph, let $\alpha(G)$ be its independence number, and let $r(G)$ be its graph radius. Graffiti's radius conjecture.

$$\alpha(G) \geq r(G)$$

The source verifies the intended bound for the listed graph classes from $r(G)\leq\operatorname{diam}(G)\leq 3\leq\alpha(G)$, but does not state that Graffiti's conjecture is solved in general.