We study the quasibound states in a graphene quantum-dot structure generated by the single-, double-, and triple-barrier electrostatic potentials. It is shown that the strongest quasibound states are mainly determined by the innermost barrier. Specifically, the positions of the quasibound states are determined by the barrier height, the number of the quasibound states is determined by the quantum-dot radius and the angular momentum, and the localization degree of the quasibound states is influenced by the width of the innermost barrier, as well as the outside barriers. Furthermore, according to the study on the double- and triple-barrier quantum dots, we find that an effective way to generate more quasibound states with even larger energy level spacings is to design a quantum dot defined by many concentric barriers with larger barrier-height differences. Last, we extend our results into the quantum dot of many barriers, which gives a complete picture about the formation of the quasibound states in the kind of graphene quantum dot created by many concentric potential barrier rings.
