  The present paper deals with the gravitational collapse of an inhomogeneous
spherical star consisting of dust fluid in the background of dark energy
components with linear equation of state. We discussed the development of
apparent horizon to investigate the black-hole formation in gravitational
collapsing process. The collapsing process is examined first separately for
dust cloud and dark energy and then under the combined effect of dust
interacting with dark energy. It is obtained that when only dust cloud or dark
energy is present the collapse leads to the formation of black-hole under
certain conditions. When both of them are present, collapsing star does not
form black-hole. However when dark energy is considered as cosmological
constant, the collapse leads to black hole formation.
