Context : The age-velocity dispersion relation is an important tool to understand the evolution of the disc of the Andromeda galaxy ( M31 ) in comparison with the Milky Way .

Aims : We use Planetary Nebulae ( PNe ) to obtain the age-velocity dispersion relation in different radial bins of the M31 disc .

Methods : We separate the observed PNe sample based on their extinction values into two distinct age populations in the M31 disc .
The observed velocities of our high- and low-extinction PNe , which correspond to higher and lower mass progenitors respectively , are fitted in de-projected elliptical bins to obtain their rotational velocities , V _ { \phi } , and corresponding dispersions , \sigma _ { \phi } .
We assign ages to the two PNe populations by comparing central-star properties of an archival sub-sample of PNe , having models fitted to their observed spectral features , to stellar evolution tracks .

Results : For the high- and low-extinction PNe , we find ages of \sim 2.5 Gyr and \sim 4.5 Gyr respectively , with distinct kinematics beyond a deprojected radius R _ { GC } = 14 kpc .
At R _ { GC } =17–20 kpc , which is the equivalent distance in disc scale lengths of the Sun in the Milky Way disc , we obtain \sigma _ { \phi,~ { } 2.5 ~ { } Gyr } = 61 \pm 14 km s ^ { -1 } and \sigma _ { \phi,~ { } 4.5 ~ { } Gyr } = 101 \pm 13 km s ^ { -1 } .
The age-velocity dispersion relation for the M31 disc is obtained in two radial bins , R _ { GC } =14–17 and 17–20 kpc .

Conclusions : The high- and low-extinction PNe are associated with the young thin and old thicker disc of M31 respectively , whose velocity dispersion values increase with age .
These values are almost twice and thrice that of the Milky Way disc stellar population of corresponding ages .
From comparison with simulations of merging galaxies , we find that the age-velocity dispersion relation in the M31 disc measured using PNe is indicative of a single major merger that occurred 2.5 – 4.5 Gyr ago with an estimated merger mass ratio \approx 1:5 .