AbstractFor a non-trivial connected graph 𝐺, a set 𝑆 ⊆ 𝑉 (𝐺) is called an edge geodetic set of 𝐺 if every edge of 𝐺 is contained in a geodesic joining some pair of vertices in 𝑆. The edge ...

The number of connected components in an unknown parent graph is to be estimated by using a sampled subgraph. This problem is first discussed for two kinds of parent graph: a transitive graph and a ...