Directed Graphclass: adjoint

The following definitions are equivalent:
  1. Let $H=(X,V)$ be a directed graph, possibly with multi-edges. The adjoint $G=(V,U)$ of $H$ has vertex set $V$ and $x\rightarrow y$ is an arc in $G$ iff the terminal endpoint of $x$ in $H$ is the initial endpoint of $y$ in $H$.
    A directed graph $G$ is an adjoint if there is some directed graph $H$ such that $G$ is the adjoint of $H$.
  2. Let $N^+(x)$ be the out-neighbourhood of $x$.
    A directed graph $G$ is an adjoint iff for any two vertices $x,y$ of $G$: If $N^+(x) \cap N^+(y) \neq\emptyset$ then $N^+(x) = N^+(y)$.

References

[90]
C. Berge
Graphs and Hypergraphs
North--Holland, Amsterdam 1985

Related classes

Inclusions

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Unweighted problems

Graph isomorphism
[?]
Input: Graphs G and H in this class
Output: True iff G and H are isomorphic.
Unknown to ISGCI [+]Details
Hamiltonian cycle
[?]
Input: A graph G in this class.
Output: True iff G has a simple cycle that goes through every vertex of the graph.
Polynomial [+]Details
Hamiltonian path
[?]
Input: A graph G in this class.
Output: True iff G has a simple path that goes through every vertex of the graph.
Unknown to ISGCI [+]Details
Recognition
[?]
Input: A graph G.
Output: True iff G is in this graph class.
Polynomial [+]Details

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