ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory


Discussiones Mathematicae Graph Theory 30(4) (2010) 671-685
DOI: 10.7151/dmgt.1522


Manoj Changat,  Joseph Mathews

Department of Futures Studies
University of Kerala, Trivandrum, India

Iztok Peterin

Institute of Mathematics and Physics, FEECS
University of Maribor, Smetanova 17, 2000 Maribor, Slovenia

Prasanth G. Narasimha-Shenoi

Department of Mathematics, Government College, Chittur
Palakkad - 678 104, India


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.

2000 Mathematics Subject Classification: 52A01, O5C12.


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Received 11 November 2009
Accepted 2 March 2010