  An effective approach for energy conservation in wireless sensor networks is
scheduling sleep intervals for extraneous nodes while the remaining nodes stay
active to provide continuous service. For the sensor network to operate
successfully the active nodes must maintain both sensing coverage and network
connectivity, It proved before if the communication range of nodes is at least
twice the sensing range, complete coverage of a convex area implies
connectivity among the working set of nodes. In this paper we consider a
rectangular region A = a *b, such that R a R b s s {\pounds}, {\pounds}, where
s R is the sensing range of nodes. and put a constraint on minimum allowed
distance between nodes(s). according to this constraint we present a new lower
bound for communication range relative to sensing range of sensors(s 2 + 3 *R)
that complete coverage of considered area implies connectivity among the
working set of nodes; also we present a new distribution method, that satisfy
our constraint.
