Identifying codes of the direct product of two cliques

  • Authors:
  • Douglas F. Rall;Kirsti Wash

  • Affiliations:
  • -;-

  • Venue:
  • European Journal of Combinatorics
  • Year:
  • 2014

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Abstract

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 in a graph G is denoted @c^I^D(G). It was recently shown by Gravier, Moncel and Semri that @c^I^D(K"n@?K"n)=@?3n2@?. Letting n,m=2 be any integers, we consider identifying codes of the direct product K"nxK"m. In particular, we answer a question of Klavzar and show the exact value of @c^I^D(K"nxK"m).