@article {IOPORT.05204992, author = {Zhang, Heping and Wang, Guangfu}, title = {A characterization of the interval distance monotone graphs.}, year = {2007}, journal = {Discrete Mathematics}, volume = {307}, number = {21}, issn = {0012-365X}, pages = {2622-2627}, publisher = {Elsevier Science B.V. (North-Holland), Amsterdam}, doi = {10.1016/j.disc.2006.11.010}, abstract = {Summary: A simple connected graph $G$ is said to be interval distance monotone if the interval $I(u,v)$ between any pair of vertices $u$ and $v$ in $G$ induces a distance monotone graph. {\it M. A\"{\i}der} and {\it M. Aouchiche} [Discrete Math. 245, 55--62 (2002; Zbl 0993.05063)] proposed the following conjecture: a graph $G$ is interval distance monotone if and only if each of its intervals is either isomorphic to a path or to a cycle or to a hypercube. In this paper we verify the conjecture.}, identifier = {05204992}, }