General bounds for identifying codes in some infinite regular graphs (Q5954312)

Summary: Consider a connected undirected graph \(G=(V,E)\) and a subset of vertices \(C\). If for all vertices \(v \in V\), the sets \(B_r(v) \cap C\) are all nonempty and pairwise distinct, where \(B_r(v)\) denotes the set of all points within distance \(r\) from \(v\), then we call \(C\) an \(r\)-identifying code. We give general lower and upper bounds on the best possible density of \(r\)-identifying codes in three infinite regular graphs.