▾ Set of symbols
▾ Alphabet
▾ Deduction system
▾ Theory
▾ Zermelo-Fraenkel set theory
▾ Set
▾ Subset
▾ Power set
▾ Hyperpower set sequence
▾ Hyperpower set
▾ Hypersubset
▾ Subset algebra
▾ Subset structure
▾ Hypergraph
▾ Graph
▾ Path graph
▾ Finite path graph
▾ Cycle graph
▾ Set of cycle subgraphs
Acyclic graph
Formulation 0
Let $G$ be a D778: Graph such that
(i) $\text{Cycles}(G)$ is a D2744: Set of cycle subgraphs for $G$
Then $G$ is an acyclic graph if and only if \begin{equation} \text{Cycles}(G) = \emptyset \end{equation}
Child definitions
» D2749: Tree graph