An unrooted tree is a tree with no distinguished root vertex. It is also called a free tree. Choosing any vertex as a root turns an unrooted tree into a rooted tree. Forgetting the root vertex of a rooted tree recovers its underlying unrooted tree. In most graph-theory contexts, the unqualified word "tree" means an unrooted tree (Skiena 1990, p. 107).
Unrooted Tree
See also
Root Vertex, Rooted Tree, TreeExplore with Wolfram|Alpha
References
Harary, F. and Palmer, E. M. "Unrooted Trees." §3.2 in Graphical Enumeration. New York: Academic Press, pp. 55-59, 1973.Knuth, D. E. The Art of Computer Programming, Vol. 1: Fundamental Algorithms, 3rd ed. Reading, MA: Addison-Wesley, 1997.Skiena, S. Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, 1990.Referenced on Wolfram|Alpha
Unrooted TreeCite this as:
Weisstein, Eric W. "Unrooted Tree." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/UnrootedTree.html