TY  - JOUR
ID  - Changat2023
LB  - Changat2023
AU  - Changat, Manoj
AU  - Sheela, Lekshmi Kamal K.
AU  - Narasimha-Shenoi, Prasanth G.
TI  - Axiomatic characterizations of Ptolemaic and chordal graphs
ST  - Axiomatic characterizations of Ptolemaic and chordal graphs
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2023
VL  - 43
IS  - 3
SP  - 393
EP  - 407
DO  - https://doi.org/10.7494/OpMath.2023.43.3.393
UR  - https://doi.org/10.7494/OpMath.2023.43.3.393
AB  - The interval function and the induced path function are two well studied class of set functions of a connected graph having interesting properties and applications to convexity, metric graph theory. Both these functions can be framed as special instances of a general set function termed as a transit function defined on the Cartesian product of a non-empty set \(V\) to the power set of \(V\) satisfying the expansive, symmetric and idempotent axioms. In this paper, we propose a set of independent first order betweenness axioms on an arbitrary transit function and provide characterization of the interval function of Ptolemaic graphs and the induced path function of chordal graphs in terms of an arbitrary transit function. This in turn gives new characterizations of the Ptolemaic and chordal graphs.
KW  - interval function
KW  - betweenness axioms
KW  - Ptolemaic graphs
KW  - transit function
KW  - induced path transit function
SN  - 1232-9274
ER  -