An algebraic characterization of geodetic graphs
Ladislav Nebeský (1998)
Czechoslovak Mathematical Journal
Similarity:
We say that a binary operation is associated with a (finite undirected) graph (without loops and multiple edges) if is defined on and if and only if , and for any , . In the paper it is proved that a connected graph is geodetic if and only if there exists a binary operation associated with which fulfils a certain set of four axioms. (This characterization is obtained as an immediate consequence of a stronger result proved in the paper).