nonbranching

Nonbranching is the adjective used to describe something that does not split into multiple branches or paths. In general, it denotes a linear, single-path structure or process, as opposed to a branched or hierarchical form.

In mathematics and graph theory, a nonbranching path is a path in which internal vertices have degree two, so the path does not branch between endpoints. In metric geometry, a non-branching space is a type of geometric space in which geodesics do not split or converge into distinct geodesics after a point; this property simplifies analysis and has implications for problems in optimal transport.

In biology and botany, nonbranching growth describes plants or plant parts that grow as a single stem without lateral branches. This growth form can be found in certain trees, shrubs, or cultivated varieties and affects architecture, light capture, and reproduction.

In chemistry, nonbranching (or linear) polymers lack side chains, yielding a straight-chain molecule; this contrasts with branched polymers. The absence of branching influences properties such as viscosity, crystallinity, and melting point.