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 £ , £ , where s R is the sensing
range of nodes. and put a constraint on minimum
allowed distance between nodes( s R ). 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.