 A rooted forest may be directed, called a directed rooted forest, either making all its edges point away from the root in each rooted tree—in which case it is called a branching or out-forest—or making all its edges point towards the root in each rooted tree—in which case it is called an anti-branching or in-forest.The term "tree" was coined in 1857 by the British mathematician Arthur Cayley.A "tree" is an undirected graph "G" that satisfies any of the following equivalent conditions