\(n\)-ary transit functions in graphs. (English) Zbl 1217.05081

Changat, Manoj; Mathews, Joseph; Peterin, Iztok; Narasimha-Shenoi, Prasanth G.

Discuss. Math., Graph Theory 30, No. 4, 671-685 (2010).

Summary: \(n\)-ary transit functions are introduced as a generalization of binary (2-ary) transit functions. We show that they can be associated with convexities in natural way and discuss the Steiner convexity as a natural \(n\)-ary generalization of geodesical convexity. Furthermore, we generalize the betweenness axioms to \(n\)-ary transit functions and discuss the connectivity conditions for the underlying hypergraph. Also, an \(n\)-ary transit function for all paths is considered.

MSC:

05C12	Distance in graphs
52A01	Axiomatic and generalized convexity

Keywords:

\(n\)-arity; transit function; betweenness; Steiner convexity