The discovery of magnetism in carbon structures containing zigzag edges has stimulated new directions in the development and design of spintronic devices. However, many of the proposed structures are designed without incorporating a key phenomenon known as topological frustration, which leads to localized non-bonding states (free radicals), increasing chemical reactivity and instability. By applying graph theory, we demonstrate that topological frustrations can be avoided while simultaneously preserving spin ordering, thus providing alternative spintronic designs. Using tight-binding calculations, we show that all original functionality is not only maintained but also enhanced, resulting in the theoretically highest performing devices in the literature today. Furthermore, it is shown that eliminating armchair regions between zigzag edges significantly improves spintronic properties such as magnetic coupling.