Unit-length Rectangular Drawings of Graphs

A rectangular drawing of a planar graph G is in which vertices are mapped to grid points, edges horizontal and vertical straight-line segments, faces drawn as rectangles. Sometimes this latter constraint relaxed for the outer face. In paper, we study drawings have unit length. We show complexity dichotomy problem deciding existence unit-length drawing, depending on whether face must also be rectangle or not. Specifically, prove that $$\textsf{NP}$$ -complete biconnected graphs when not required rectangle, even if sought respect given embedding, whereas it polynomial-time solvable, both fixed variable embedding settings, rectangle.