  For a graph $G$, Chartrand et al. defined the rainbow connection number
$rc(G)$ and the strong rainbow connection number $src(G)$ in "G. Charand, G.L.
John, K.A. Mckeon, P. Zhang, Rainbow connection in graphs, Mathematica
Bohemica, 133(1)(2008) 85-98". They raised the following conjecture: for two
given positive $a$ and $b$, there exists a connected graph $G$ such that
$rc(G)=a$ and $src(G)=b$ if and only if $a=b\in\{1,2\}$ or $ 3\leq a\leq b$".
In this short note, we will show that the conjecture is true.
