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We investigate the conductance of an undoped graphene sheet with two metalliccontacts and an electrostatically gated island (quantum dot) between thecontacts. Our analysis is based on the Matrix Green Function formalism, whichwas recently adapted to graphene by Titov {\em et al.} [Phys.\ Rev.\ Lett.\{\bf 104}, 076802 (2010)]. We find pronounced differences between the case of astadium-shaped dot (which has chaotic classical dynamics) and a disc-shaped dot(which has integrable classical dynamics) in the limit that the dot size issmall in comparison to the distance between the contacts. In particular, forthe stadium-shaped dot the two-terminal conductance shows Fano resonances as afunction of the gate voltage, which cross-over to Breit-Wigner resonances onlyin the limit of completely separated resonances, whereas for a disc-shaped dotsharp Breit-Wigner resonances resulting from higher angular momentum remainpresent throughout.

Resonant scattering in graphene with a gate-defined chaotic quantum dot