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arXiv · 2005.06751

The Interval function, Ptolemaic, distance hereditary, bridged graphs and axiomatic characterizations

Manoj Changat·Lekshmi Kamal K. Sheela·Prasanth G. Narasimha-Shenoi
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Abstract

In this paper we consider certain types of betweenness axioms on the interval function $I_G$ of a connected graph $G$. We characterize the class of graphs for which $I_G$ satisfy these axioms. The class of graphs that we characterize include the important class of Ptolemaic graphs and some proper superclasses of Ptolemaic graphs: the distance hereditary graphs and the bridged graphs. We also provide axiomatic characterizations of the interval function of these classes of graphs using an arbitrary function known as \emph{transit function}.

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Manoj Changat, Lekshmi Kamal K. Sheela, Prasanth G. Narasimha-Shenoi. 2020-05-14. The Interval function, Ptolemaic, distance hereditary, bridged graphs and axiomatic characterizations. https://arxiv.org/abs/2005.06751

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