Geodesic
On Antipodal and Diametrical Partial Cubes
Discussiones Mathematicae. Graph Theory, Tome 41 (2021) no. 4, pp. 1127-1145

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We prove that any diametrical partial cube of diameter at most 6 is antipodal. Because any antipodal graph is harmonic, this gives a partial answer to a question of Fukuda and Handa [Antipodal graphs and oriented matroids, Discrete Math. 111 (1993) 245–256] whether any diametrical partial cube is harmonic, and improves a previous result of Klavžar and Kovše [On even and harmonic-even partial cubes, Ars Combin. 93 (2009) 77–86].
Keywords: diametrical graph, harmonic graph, antipodal graph, partial cube, diameter, isometric dimension 
Polat, Norbert. On Antipodal and Diametrical Partial Cubes. Discussiones Mathematicae. Graph Theory, Tome 41 (2021) no. 4, pp. 1127-1145. http://geodesic.mathdoc.fr/item/DMGT_2021_41_4_a17/
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