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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1522,
author = {Manoj Changat and Joseph Mathews and Iztok Peterin and Prasanth G. Narasimha-Shenoi},
title = {n-ary transit functions in graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {30},
year = {2010},
pages = {671-685},
zbl = {1217.05081},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1522}
}
Manoj Changat; Joseph Mathews; Iztok Peterin; Prasanth G. Narasimha-Shenoi. n-ary transit functions in graphs. Discussiones Mathematicae Graph Theory, Tome 30 (2010) pp. 671-685. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1522/
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