On Some Properties of Antipodal Partial Cubes

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(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
• 05c12
• 05c75