On Antipodal and Diametrical Partial Cubes

On Antipodal and Diametrical Partial Cubes

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 ha...

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Bibliographic Details
Main Author: Polat Norbert
Format: Article
Language:English
Published: Sciendo 2021-11-01
Series:Discussiones Mathematicae Graph Theory
Subjects:
diametrical graph
harmonic graph
antipodal graph
partial cube
diameter
isometric dimension
05c12
05c75
Online Access:https://doi.org/10.7151/dmgt.2305
Description
Summary: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].
ISSN:2083-5892

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