DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

IMPACT FACTOR 2018: 0.741

SCImago Journal Rank (SJR) 2018: 0.763

Rejection Rate (2018-2019): c. 84%

Discussiones Mathematicae Graph Theory

Article in press


Authors:

N. Polat

Title:

On antipodal and diametrical partial cubes

Source:

Discussiones Mathematicae Graph Theory

Received: 2018-11-17, Accepted: 2019-08-24, https://doi.org/10.7151/dmgt.2305

Abstract:

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

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