A sufficient condition for infinite connectivity in two dimensional ad-hoc wireless sensor networks

In this paper connectivity problem in wireless ad-hoc sensor networks is discussed. Asymptotic cases are considered. A relationship between coverage and connectivity in these networks is stated, generalized and used to find some upper bounds for transmitting capability of sensors. We introduce some concepts as multiconnectivity, infinite-connectivity and discuss their relation to fault tolerance in a sensor network. A sufficient condition for the order of connectivity to grow faster than the number of nodes is declared and proven.