Are Yao Graph and Theta Graph Void Free?

Greedy Forwarding algorithm is a widely-used routing algorithm for wireless networks. However, it can fail if network topologies (usually modeled by geometric graphs) contain voids. Since Yao Graph and Theta Graph are two types of geometric graphs exploited to construct wireless network topologies, this paper studies whether these two types of graphs can contain voids. Specifically, this paper shows that when the number of cones in a Yao Graph or Theta Graph is less than 6, Yao Graph and Theta Graph can have voids, but when the number of cones equals or exceeds 6, Yao Graph and Theta Graph are free of voids.