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- W2020126254 abstract "A set S of vertices of a graph G is a dominating set of G if every vertex u of G is either in S or it has a neighbour in S . In other words, S is dominating if the sets S ∩ N [ u ] where u ∈ V ( G ) and N [ u ] denotes the closed neighbourhood of u in G , are all nonempty. A set S ⊆ V ( G ) is called a locating code in G , if the sets S ∩ N [ u ] where u ∈ V ( G ) ∖ S are all nonempty and distinct. A set S ⊆ V ( G ) is called an identifying code in G , if the sets S ∩ N [ u ] where u ∈ V ( G ) are all nonempty and distinct. We study locating and identifying codes in the circulant networks C n ( 1 , 3 ) . For an integer n ⩾ 7 , the graph C n ( 1 , 3 ) has vertex set Z n and edges x y where x , y ∈ Z n and | x − y | ∈ { 1 , 3 } . We prove that a smallest locating code in C n ( 1 , 3 ) has size ⌈ n / 3 ⌉ + c , where c ∈ { 0 , 1 } , and a smallest identifying code in C n ( 1 , 3 ) has size ⌈ 4 n / 11 ⌉ + c ′ , where c ′ ∈ { 0 , 1 } ." @default.
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- W2020126254 date "2013-09-01" @default.
- W2020126254 modified "2023-09-27" @default.
- W2020126254 title "Locating and identifying codes in circulant networks" @default.
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- W2020126254 doi "https://doi.org/10.1016/j.dam.2013.03.008" @default.
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