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.
- Interval distance monotonicity
- Metric properties
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics