  During the evolution of proto-planetary disc, photo-evaporations of both
central and external stars play important roles. Considering the complicated
radiation surroundings in the clusters, where the star formed, the
proto-planetary discs survive in different lifetimes due to flyby events. In
this paper, we mainly focus on the disc around a T Tauri star, which encounters
with another main-sequence star with different temperatures in hyperbolic
orbits with different peri-center distances, eccentricities and inclinations.
We find the criterion for gap-opening due to photo-evaporation of central star
after the flyby event. A gap is opened in the late stage of gas disc, and
induce that the gap only influence the planet formation and migration
limitedly. If the flyby orbit has a moderate value of peri-center distance,
which weakly depends on the eccentricity and inclination, the external
photo-evaporation lead to a maximum mass loss during the flyby event. Flyby
stars in orbits with smaller eccentricities or larger inclinations induce
larger mass loss. Adopting a simple multiple flyby models, we conclude that in
open clusters, gas discs usually survive in typical lifetimes between 1 and 10
Myr, except there are many massive stars in dense open clusters. In globular
clusters, discs disperse very quickly and hardly produce the gas giant planets.
The fast-depleted discs are probably responsible for the null detection of
giant planets in globular clusters.
