Math 2.0

Combinatorics Definition

Acyclic graph

Builds on Cycle

Definition

A graph is acyclic if it has no cycle.

Remarks

An acyclic graph is also called a forest. A connected acyclic graph is a tree. The path graphs and the graphs with no edges are acyclic. The cycle graphs are not. A finite acyclic graph with nn vertices and cc components has n−cn - c edges.

Reading path

To understand this page from the ground up, read these 6 pages in order. The foundations come first.

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Graph, definition, no evidence levelGraphdefinitionWalk, definition, no evidence levelWalkdefinitionTrail, definition, no evidence levelTraildefinitionCircuit, definition, no evidence levelCircuitdefinitionCycle, definition, no evidence levelCycledefinitionAcyclic graph, definition, no evidence levelAcyclic graphdefinition
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. Trail definition
  4. Circuit definition
  5. Cycle definition
  6. Acyclic graph definition

Where this leads

16 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Tree_(graph_theory), Forest
About this page
Tag0XNN9Z8E5A
URIm2://0XNN9Z8E5A
Kinddefinition
WritingW1 stated
MSC05C05
DefinesAcyclic graph
UsesCycle

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