Summary: R. C. Brigham et al. [Math. Bohem. 128, No. 1, 25–36 (2003; Zbl 1010.05048)] derived some lower and upper bounds of the metric-location-domination number \(\gamma_M(G)\) of any connected graph \(G\); namely, \(\max\{\beta(G),\gamma(G)\}\le\gamma_M(G)\le \min\{\beta(G)+\gamma(G),n-1\}\). In this paper, we discuss graphs \(G\) which attain the lower or upper bounds.