The axiomatic characterization of the interval function of distance hereditary graphs.

A connected graph G is distance hereditary if every induced path in G is a shortest path. The Interval function I G (u , v) of a connected graph G is defined as the set of all vertices that lie on some shortest u , v -path in G. In this paper, we consider certain types of first-order betweenness axioms framed on an arbitrary function known as transit function and used to characterize the interval function I G of a distance hereditary graph. As a byproduct, we give a new characterization of distance hereditary graphs using these betweenness axioms. [ABSTRACT FROM AUTHOR]