ID Codes in Cartesian Products of Cliques
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چکیده
An identifying code in a graph G is a set D of vertices such that the closed neighborhood of each vertex of the graph has a nonempty, distinct intersection with D. The minimum cardinality of an identifying code is denoted γ(G). Building upon recent results of Gravier, Moncel, and Semri, we show for n ≤ m that γID(Kn Km) = max{2m−n,m+⌊n/2⌋}. Furthermore, we improve upon the bounds for γ(G Km) and explore the specific case when G is the Cartesian product of multiple cliques. Dedicated to Kieka Mynhardt with thanks
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تاریخ انتشار 2013