Distance monotonicity and a new characterization of hypercubes Original Research Article

In this paper, we are interested in some metric properties of graphs. In particular, we investigate distance monotonicity in graphs. Straightaway, we revisit the notion of distance monotonicity. We then introduce interval distance monotone graphs, graphs which are not distance monotone but whose intervals are distance monotone. Finally, we obtain a new characterization of hypercubes involving this notion.