Editing Rooted graph (section)

In [[mathematics]], and, in particular, in [[graph theory]], a '''rooted graph''' is a [[Graph (discrete mathematics)|graph]] in which one [[vertex (graph theory)|vertex]] has been distinguished as the root.<ref>{{citation|first=Daniel|last=Zwillinger|title=CRC Standard Mathematical Tables and Formulae, 32nd Edition|year=2011|publisher=CRC Press|isbn=978-1-4398-3550-0|page=150}}</ref><ref>{{citation
 | last = Harary | first = Frank | author-link = Frank Harary
 | doi = 10.1090/S0002-9947-1955-0068198-2
 | journal = [[Transactions of the American Mathematical Society]]
 | mr = 0068198
 | pages = 445–463
 | title = The number of linear, directed, rooted, and connected graphs
 | volume = 78
 | year = 1955| issue = 2 | doi-access = free
 }}. See p.&nbsp;454.</ref>  Both [[directed graph|directed]] and [[undirected graph|undirected]] versions of rooted graphs have been studied, and there are also variant definitions that allow multiple roots.

[[File:Rooted graphs.png|thumb|300px|Examples of rooted graphs with some variants. A digraph with the root placed such that each vertex has exactly one path directed to it from the root is an [[arborescence (graph theory)|arborescence]].]]
 
Rooted graphs may also be known (depending on their application) as '''pointed graphs''' or '''flow graphs'''. In some of the applications of these graphs, there is an additional requirement that the whole graph be [[Reachability|reachable]] from the root vertex.