Title: Median graphs and algebras

Abstract: In this talk we present a strong connection between certain ternary algebras, called median algebras, that enjoy three simple axioms, and the class of median graphs. The latter are defined as the graphs in which for any triple of vertices the three intervals between pairs of the triple share exactly one vertex. Median graphs are the most important class in metric graph theory, and appear in several applications in Computer science, mathematical biology and elsewhere.

We select a small portion of numerous characterizations and properties of median graphs, with an emphasis on some recent results.