Geodesic
On Some Properties of Antipodal Partial Cubes
Discussiones Mathematicae. Graph Theory, Tome 40 (2020) no. 3, pp. 755-770

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We prove that an antipodal bipartite graph is a partial cube if and only it is interval monotone. Several characterizations of the principal cycles of an antipodal partial cube are given. We also prove that an antipodal partial cube G is a prism over an even cycle if and only if its order is equal to 4(diam(G) − 1), and that the girth of an antipodal partial cube is less than its diameter whenever it is not a cycle and its diameter is at least equal to 6.
Keywords: antipodal graph, partial cube, interval monotony, girth, diameter 
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Polat, Norbert. On Some Properties of Antipodal Partial Cubes. Discussiones Mathematicae. Graph Theory, Tome 40 (2020) no. 3, pp. 755-770. http://geodesic.mathdoc.fr/item/DMGT_2020_40_3_a3/