# Abstract for the talk at 07.05.2013 (15:15 h)

**VW Seminar**

*Manoj Changat*(University of Kerala, India)

**Transit functions and associated convexity notions on graphs**

Transit functions or interval functions are introduced to generalize and axiomatic three basic notions in Mathematics: the interval, convexity and betweenness. The basic transit axioms which define a transit function can be interpreted as simple betweenness properties. Well studied transit functions on graphs, namely the geodesic interval function, the induced path transit functions and other transit functions and their associated convexities are discussed. Also some examples of transit functions from Recombination theory are discussed. The betweenness axioms that hold for the interval function and the induced path transit function in general for an arbitrary connected graph as well as those which may not hold for an arbitrary graph is discussed. Two types of problems that arises in this context naturally is mentioned. They are (i) Characterize the class of graphs for which a particular type of betweenness axiom hold for the interval function or induced path function or some other function. (ii) Characterize the interval function or induced path transit function of some special classes of graphs using some betweenness axioms defined on an arbitrary transit function.