Authors:
N. Polat
Title:
On some properties of antipodal partial cubes
Source:
Discussiones Mathematicae Graph Theory
Received 13.10.2017, Revised 21.02.2018, Accepted 09.04.2018, doi: 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

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