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

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n-ary TRANSIT FUNCTIONS IN GRAPHS

Manoj Changat,  Joseph Mathews

Department of Futures Studies
University of Kerala, Trivandrum, India
e-mail: mchangat@gmail.com
e-mail: jose_chingam@yahoo.co.in

Iztok Peterin

Institute of Mathematics and Physics, FEECS
University of Maribor, Smetanova 17, 2000 Maribor, Slovenia
e-mail: iztok.peterin@uni-mb.si

Prasanth G. Narasimha-Shenoi

Department of Mathematics, Government College, Chittur
Palakkad - 678 104, India
e-mail: gnprasanth@gmail.com

Abstract

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