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An effective approach for energy conservation in wireless sensor networks isscheduling sleep intervals for extraneous nodes while the remaining nodes stayactive to provide continuous service. For the sensor network to operatesuccessfully the active nodes must maintain both sensing coverage and networkconnectivity, It proved before if the communication range of nodes is at leasttwice the sensing range, complete coverage of a convex area impliesconnectivity among the working set of nodes. In this paper we consider arectangular region A = a *b, such that R a R b s s {\pounds}, {\pounds}, wheres R is the sensing range of nodes. and put a constraint on minimum alloweddistance between nodes(s). according to this constraint we present a new lowerbound for communication range relative to sensing range of sensors(s 2 + 3 *R)that complete coverage of considered area implies connectivity among theworking set of nodes; also we present a new distribution method, that satisfyour constraint.

A New Sufficient Condition for 1-Coverage to Imply Connectivity