Math 2.0

definition

Spanning tree

Definition

Let GG be a graph. A spanning tree of GG is a subgraph TT of GG that contains every vertex of GG and is a tree.

Remarks

A graph has a spanning tree if and only if it is connected. The node every connected graph has a spanning tree gives one direction. A spanning tree of a finite connected graph with nn vertices has n−1n - 1 edges. The complete graph KnK_n has nn−2n^{n-2} spanning trees, by Cayley's formula. A minimum spanning tree has the least total weight.

Explanations

L1 human

A spanning tree keeps all the vertices of a graph and just enough edges to stay connected without any loop. For a road network, it is a smallest set of roads that still links all towns.

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)

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What this needs

To read this node, read these 11 nodes in this order. The foundations come first, and the list ends with this node.

Graph, definition, no evidence levelGraphdefinitionSubgraph, definition, no evidence levelSubgraphdefinitionWalk, 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 levelTreedefinitionSpanning tree, definition, no evidence levelSpanning treedefinition
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. Subgraph definition
  3. Walk definition
  4. Reachability definition
  5. Trail definition
  6. Connected graph definition
  7. Circuit definition
  8. Cycle definition
  9. Acyclic graph definition
  10. Tree definition
  11. Spanning tree definition

What depends on this

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

Sources

  1. Web https://en.wikipedia.org/wiki/Spanning_tree, Definitions

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