A disjoint union of paths is called a linear forest.

Paths are fundamental concepts of graph theory, described in the introductory sections of most graph theory texts.

See, for example, Bondy and Murty (1976), Gibbons (1985), or Diestel (2005).

In algebra, path graphs appear as the Dynkin diagrams of type A.

As such, they classify the root system of type A and the Weyl group of type A, which is the symmetric group.