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On some non-obvious connections between graphs and unary partial algebras. (English) Zbl 1046.08002
For an undirected graph two types of subgraphs are defined, namely a weak subgraph and a relative subgraph. For a digraph, moreover, a strong subdigraph and a dually strong subdigraph are defined. Further, partial unary algebras are studied. To any such algebra \(A\) its graph \(G^*(A)\) and its digraph \(G(A)\) are assigned in a natural way. Four types of subalgebras (analogous to the types of subdigraphs) are defined, namely weak subalgebras, relative subalgebras, strong subalgebras and initial segments. Lattices of such subgraphs and subalgebras are studied and interconnections between isomorphisms of those lattices and isomorphisms of corresponding algebras and their graphs and digraphs are investigated.

MSC:
08A55 Partial algebras
08A60 Unary algebras
05C20 Directed graphs (digraphs), tournaments
05C75 Structural characterization of families of graphs
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