Identifying codes and locating–dominating sets on paths and cycles

Let G = ( V , E ) be a graph and let r ≥ 1 be an integer. For a set D ⊆ V , define N r [ x ] = { y ∈ V : d ( x , y ) ≤ r } and D r ( x ) = N r [ x ] ∩ D , where d ( x , y ) denotes the number of edges in any shortest path between x and y . D is known as an r -identifying code ( r -locating-dominatin...

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