The first incident occurred around 12.20am on Dunlop Street where a Vauxhall Astra was deliberately set alight.
The second incident occurred around 4.15am on East Hamilton Street, where two cars, a Fiat 500 and a Vauxhall Corsa, were targeted and set on fire.
Officers believe the incidents are linked and are appealing for further information.
Detective Inspector Neil Martin said: “The fires have caused substantial damage to the vehicles involved. I am asking anyone who was in the area in the early hours of this morning to contact us. In particular, I would appeal to taxi drivers and other motorists who may have dash cams to check their footage as it could hold images which could prove significant to our enquiries.”
Anyone with information is asked to call Police Scotland via 101, quoting incident numbers 0079 and 0661 of 23 April, 2023. Alternatively, please contact Crimestoppers on 0800 555 111 where information can be given anonymously.
