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# acyclic graph

Any graph that contains no cycles is an *acyclic graph*. A directed acyclic graph is often called a DAG for short.

$\begin{array}[]{cc}\xymatrix{\hfil&A\ar@{-}[dl]\ar@{-}[dr]\\ B&&C&\xymatrix{&A\ar[dr]\\ B\ar[ur]\ar[rr]&&C\end{array}$ |

In contrast, the following graph and digraph are *not* acyclic, because
each contains a cycle.

$\begin{array}[]{cc}\xymatrix{\hfil&A\ar@{-}[dl]\ar@{-}[dr]\\ B\ar@{-}[rr]&&C&\xymatrix{&A\ar[dr]\\ B\ar[ur]&&C\ar[ll]\end{array}$ |

Defines:

directed acyclic graph

Related:

Graph,Cycle, BetheLattice

Synonym:

acyclic, DAG

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

05C38*no label found*

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new question: Prime numbers out of sequence by Rubens373

Oct 7

new question: Lorenz system by David Bankom

Oct 19

new correction: examples and OEIS sequences by fizzie

Oct 13

new correction: Define Galois correspondence by porton

Oct 7

new correction: Closure properties on languages: DCFL not closed under reversal by babou

new correction: DCFLs are not closed under reversal by petey

Oct 2

new correction: Many corrections by Smarandache

Sep 28

new question: how to contest an entry? by zorba

new question: simple question by parag