Zero-one law for connectivity in superposition of random key graphs on random geometric graphs (Q1723597)

Summary: We study connectivity property in the superposition of random key graph on random geometric graph. For this class of random graphs, we establish a new version of a conjectured zero-one law for graph connectivity as the number of nodes becomes unboundedly large. The results reported here strengthen recent work by the \textit{B. S. Krishnan} et al. [``On connectivity thresholds in superposition of random key graphs on random geometric graphs'', in: Proceedings of the IEEE international symposium on information theory, ISIT '13. Piscataway, NJ: IEEE. 2389--2393 (2013; \url{doi:10.1109/ISIT.2013.6620654})].