General Bounds for Identifying Codes in Some Infinite Regular Graphs

Irène Charon, Iiro Honkala, Olivier Hudry, Antoine Lobstein

Abstract


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.


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