On Minimum Identifying Codes in Some Cartesian Product Graphs

نویسندگان

  • Douglas F. Rall
  • Kirsti Wash
چکیده

An identifying code in a graph is a dominating set that also has the property that the closed neighborhood of each vertex in the graph has a distinct intersection with the set. The minimum cardinality of an identifying code, or ID code, in a graph G is called the ID code number of G and is denoted γ(G). In this paper, we give upper and lower bounds for the ID code number of the prism of a graph, or G2K2. In particular, we show that γ(G2K2) ≥ γ(G) and we show that this bound is sharp. We also give upper and lower bounds for the ID code number of grid graphs and a general upper bound for γ(G2K2).

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عنوان ژورنال:
  • Graphs and Combinatorics

دوره 33  شماره 

صفحات  -

تاریخ انتشار 2017