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Single-atom catalysts have the advantage of high chemical efficiency, which requires atomic-scale control during catalyst formation. In order to address this challenge, this work explores the synthesis of single-atom platinum (SA-Pt) catalysts using atomic-layer deposition (ALD) on vertical graphene (VG), in which a large number of graphene edges serve as energetically favorable nucleation sites for SA-Pt, as predicted by density functional theory calculations. Interestingly, SA-Pt has been achieved on VGs at low ALD cycle numbers of up to 60. With a further increase in the number of ALD cycles, an increasing number of Pt clusters with diameters <2 nm and Pt nanoparticles (NPs) with diameters >2 nm become dominant (nano-Pt @VG). This is in contrast to the observation of predominantly nano-Pt on other carbon nanostructures, such as carbon nanotubes and monolayer graphene, under the same ALD growth conditions, indicating that the edge states on VG indeed play a critical role in facilitating the formation of SA-Pt. Profound differences are revealed in a comparative study on H2 sensing. SA-Pt exhibits both a higher sensitivity and faster response than its nano-Pt counterpart by more than an order of magnitude, illustrating the high catalytic efficiency of SAPt and its potential for gas sensing and a variety of other catalytic applications.