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