A sufficient condition for a bipartite graph to be a cube

Two Characterizations of Hypercubes

“…Because G is connected, the result follows. As noted in [2] and [7], a graph G is a hypercube if and only if G is spherical and bipartite. We aim to substitute this condition for a graph to be spherical with a weaker condition of antipodality and with a local condition for a graph to be a (0, 2)-graph.…”

“…We give a sufficient conditions for an antipodal bipartite graph to be a regular one. First we give two basic properties of antipodal graphs (see also [7]).…”

“…We begin with some basic properties of antipodal graphs (see also [7]). Then we prove that a graph is a hypercube if and only if it is an antipodal, bipartite (0, 2)graph.…”