A graph
is called
-dominated
if it satisfies
for every pair
of vertices at distance 2, where
,
and
if
, then
for
at distance
}. For a noncomplete graph
, the number
is defined as
:
and
, for a complete graph
, set
. In this paper, we prove that a 2-connected
-dominated graph
of order
is hamiltonian if
and
, moreover it is best possible.