Adjoint digraph

Adjoint digraph — сопряженный орграф.

The adjoint digraph is defined as a graph, that is, the one whose arcs are exactly the converses for those of [math]\displaystyle{ \,G }[/math]. The adjacency operator [math]\displaystyle{ A(G^{\ast}) }[/math] of [math]\displaystyle{ G^{\ast} }[/math] is the adjoint operator [math]\displaystyle{ A(G)^{\ast} }[/math]. Though [math]\displaystyle{ G^{\ast} }[/math] is called the converse digraph of [math]\displaystyle{ \,G }[/math] among graph theorists, the term adjoint is often used in this sense.

The coadjoint graphs are graphs [math]\displaystyle{ \,G }[/math] and [math]\displaystyle{ G^{\ast} }[/math] satisfying [math]\displaystyle{ G \cong G^{\ast} }[/math].