  Exact solutions of the Einstein field equations with cosmic string and space
varying cosmological constant, viz., $\Lambda= \Lambda(r)$, in the
energy-momentum tensors are presented. Three cases have been studied: where
variable cosmological constant (1) has power law dependence, (2) is
proportional to the string fluid density, and (3) is purely a constant. Some
cases of interesting physical consequences have been found out such that (i)
variable cosmological constant can be represented by a power law of the type
$\Lambda=3r^{-2}$, (ii) variable cosmological constant and cosmic string
density are interdependent to each other according to the relation
$\Lambda=-8\pi{\rho}_s$, and (iii) cosmic string density can be scaled by a
power law of the type ${\rho}_s=r^{-2}$. It is also shown that several known
solutions can be recovered from the general form of the solutions obtained
here.
