Geodesic
n-ary transit functions in graphs
Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 4, pp. 671-685.

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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 geodesicaly convexity. Furthermore, we generalize the betweenness axioms to n-ary transit functions and discuss the connectivity conditions for underlying hypergraph. Also n-ary all paths transit function is considered.
Keywords: n-arity, transit function, betweenness, Steiner convexity 
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Changat, Manoj; Mathews, Joseph; Peterin, Iztok; Narasimha-Shenoi, Prasanth. n-ary transit functions in graphs. Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 4, pp. 671-685. http://geodesic.mathdoc.fr/item/DMGT_2010_30_4_a11/

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