Editing Tree (graph theory) (section)

==Types of trees==
* A ''[[path graph]]'' (or ''linear graph'') consists of {{mvar|n}} vertices arranged in a line, so that vertices {{mvar|i}} and {{math|''i'' + 1}} are connected by an edge for {{math|1=''i'' = 1, …, ''n'' – 1}}.
* A ''[[starlike tree]]'' consists of a central vertex called ''root'' and several path graphs attached to it. More formally, a tree is starlike if it has exactly one vertex of degree greater than 2.
* A ''[[Star (graph theory)|star tree]]'' is a tree which consists of a single internal vertex (and {{math|''n'' – 1}} leaves). In other words, a star tree of order {{mvar|n}} is a tree of order {{mvar|n}} with as many leaves as possible.
* A ''[[caterpillar tree]]'' is a tree in which all vertices are within distance 1 of a central path subgraph.
* A ''[[List of graphs#Lobster|lobster tree]]'' is a tree in which all vertices are within distance 2 of a central path subgraph.
* A ''regular tree'' of degree {{mvar|d}} is the infinite tree with {{mvar|d}} edges at each vertex. These arise as the [[Cayley graph]]s of [[free group]]s, and in the theory of [[Building (mathematics)|Tits buildings]]. In [[statistical mechanics]] they are known as ''[[Bethe lattice]]s''.