# DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

# IMPACT FACTOR 2019: 0.755

SCImago Journal Rank (SJR) 2019: 0.600

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

# Discussiones Mathematicae Graph Theory

Article in press

Authors:

N. Polat

Title:

On some properties of antipodal partial cubes

Source:

Discussiones Mathematicae Graph Theory

Received: 2017-10-13, Revised: 2018-02-21, Accepted: 2018-04-09, https://doi.org/10.7151/dmgt.2146

Abstract:

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 $4(\mathrm{diam}(G)-1)$, 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