Math 2.0

definition

Tree

Definition

A tree is a graph that is connected and acyclic.

Remarks

Let TT be a finite graph with n≥1n \ge 1 vertices. Then these conditions are equivalent: TT is a tree; TT is connected with n−1n - 1 edges; TT is acyclic with n−1n - 1 edges. A graph is a tree if and only if any two vertices are joined by exactly one path. The node unique paths in trees states this. The path graphs and the stars K1,nK_{1,n} are trees.

Explanations

L1 human

A tree is a connected graph with no loops. A family tree and the folders on a computer are pictures of trees.

What this node needs for W2
  • edge instance_of in: one example (0 of 1)
  • edge not_instance_of in: one non-example that fails one clause (0 of 1)

The writing levels say how complete the text of a node is. They do not measure its truth.

What this needs

To read this node, read these 9 nodes in this order. The foundations come first, and the list ends with this node.

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 levelTreedefinition
Each node uses the nodes above it. The colour of the bar on a box shows the evidence level, and the box also gives it as text. The list below has the same nodes.
  • 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

What depends on this

11 nodes use this node, directly or through other nodes.

Sources

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

What links here

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