. Regarding the problem mentioned by Brigham et al. “Is it correct that each connected bicritical graph possesses a minimum dominating set having every two appointed vertices of graphs?”, we first give a class of graphs that disprove it and second obtain domination numbers and diameters of the graphs of this class. This class of graphs has the property: ω(H) − diam(H) → ∞ when |V(H)| = n → ∞. Also, for the bicritical graphs of this class, i(H) = ω(H).
