Some extended results on diameter-stable graphs

A graph G is said to be an ( l , d ) -graph (with respect to edges) if d ( G − E ) ≤ d , ∀ E ⊂ E ( G ) such that | E | ≤ l − 1 . The l -diameter-stable graphs are ( l , d ) -graphs with diameter d . In this paper some results given by Hartman and Rubin in [1] and a theorem obtained in [6] are extended.