Math 2.0

Combinatorics Definition

Rooted tree

Builds on Tree

Definition

A rooted tree is a pair (T,r)(T, r) of a tree TT and a vertex rr of TT, the root.

Let v≠rv \neq r be a vertex, and let uu be the neighbour of vv on the unique path from vv to rr. Then uu is the parent of vv, and vv is a child of uu. The depth of vv is the distance from rr to vv.

Remarks

The root has no parent, and every other vertex has exactly one parent. A vertex with no child is a leaf of the rooted tree. With this convention the root can be a leaf only when the tree has one vertex. An ordered rooted tree also fixes an order of the children of each vertex. A binary tree is a related recursive structure.

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To understand this page from the ground up, read these 10 pages in order. The foundations come first.

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Graph, definition, no evidence levelGraphdefinitionWalk, definition, no evidence levelWalkdefinitionReachability, definition, no evidence levelReachabilitydefinitionTrail, definition, no evidence levelTraildefinitionConnected graph, definition, no evidence levelConnected graphdefinitionCircuit, definition, no evidence levelCircuitdefinitionCycle, definition, no evidence levelCycledefinitionAcyclic graph, definition, no evidence levelAcyclic graphdefinitionTree, definition, no evidence levelTreedefinitionRooted tree, definition, no evidence levelRooted treedefinition
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Graph definition
  2. Walk definition
  3. Reachability definition
  4. Trail definition
  5. Connected graph definition
  6. Circuit definition
  7. Cycle definition
  8. Acyclic graph definition
  9. Tree definition
  10. Rooted tree definition

Where this leads

1 page builds on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Tree_(graph_theory), Rooted tree
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