The single triangle-strip loop generation algorithm on a triangulated two-manifold presented by Gopi and Eppstein [4] is based on the guaranteed existence of a perfect matching in its dual graph. However, such a perfect matching is not guaranteed in the dual graph of triangulated manifolds with boundaries. In this paper, we present algorithms that suitably modify the results of the dual graph matching to generate a single strip loop on manifolds with boundaries. Further, the algorithm presented in [4] can produce only strip loops, but not linear strips. We present an algorithm that does topological surgery to construct linear strips, with user-specified start and end triangles, on manifolds with or without boundaries. The main contributions of this paper include graph algorithms to handle unmatched triangles, reduction of the number of Steiner vertices introduced to create strip loops, and finally a novel method to generate single linear strips with arbitrary start and end positions.