Abstract
Connectivity, resilient and unsplittability are the essential requirements of any wireless sensor network (WSN). Connectivity ensures that the complete network is a single component and there exists at least one path between any two nodes, while resilient and unsplittability ensures that the network remains connected even if a linear proportion of the nodes were compromised by the adversary. In this work we consider a wireless sensor network induced by kryptograph with non-full visibility condition. We derive a threshold for transmission range above which the WSN becomes connected almost surely. We also derive threshold conditions to show resilience and unsplittability of connected sensor networks in an almost sure sense and provided simulated experiments in support of our claims.
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