  We consider the general case of an accelerating, expanding and shearing model
of a radiating relativistic star using Lie symmetries. We obtain the Lie
symmetry generators that leave the equation for the junction condition
invariant, and find the Lie algebra corresponding to the optimal system of the
symmetries. The symmetries in the optimal system allow us to transform the
boundary condition to ordinary differential equations. The various cases for
which the resulting systems of equations can be solved are identified. For each
of these cases the boundary condition is integrated and the gravitational
potentials are found explicitly. A particular group invariant solution produces
a class of models which contains Euclidean stars as a special case. Our
generalized model satisfies a linear equation of state in general. We thus
establish a group theoretic basis for our generalized model with an equation of
state. By considering a particular example we show that the weak, dominant and
strong energy conditions are satisfied.
