Identifying Codes of Lexicographic Product of Graphs

Gravier et al. investigated the identifying codes of Cartesian product of two graphs. In this paper we consider the identifying codes of lexicographic product G[H] of a connected graph G and an arbitrary graph H, and obtain the minimum cardinality of identifying codes of G[H] in terms of some parameters of G and H.

[1]  IIRO HONKALA,et al.  On identifying codes in the triangular and square grids , 2004, SIAM J. Comput..

[2]  Douglas F. Rall,et al.  Identifying codes of the direct product of two cliques , 2014, Eur. J. Comb..

[3]  Iiro S. Honkala,et al.  On Identifying Codes in Binary Hamming Spaces , 2002, J. Comb. Theory, Ser. A.

[4]  Nathalie Bertrand,et al.  Identifying and locating-dominating codes on chains and cycles , 2004, Eur. J. Comb..

[5]  Gérard D. Cohen,et al.  On identifying codes , 1999, Codes and Association Schemes.

[6]  Sylvain Gravier,et al.  Identifying Codes of Cartesian Product of Two Cliques of the Same Size , 2008, Electron. J. Comb..

[7]  S. Litsyn,et al.  On binary codes for identification , 2000 .

[8]  David R. Wood,et al.  Extremal Graph Theory for Metric Dimension and Diameter , 2007, Electron. J. Comb..

[9]  Mark G. Karpovsky,et al.  On the Covering of Vertices for Fault Diagnosis in Hypercubes , 1999, Inf. Process. Lett..

[10]  Sylvain Gravier,et al.  Identifying codes of cycles , 2006, Eur. J. Comb..

[11]  Xiao-Dong Hu,et al.  Identifying codes of cycles with odd orders , 2008, Eur. J. Comb..

[12]  Antoine Lobstein,et al.  Minimizing the size of an identifying or locating-dominating code in a graph is NP-hard , 2003, Theor. Comput. Sci..

[13]  Mark G. Karpovsky,et al.  On a New Class of Codes for Identifying Vertices in Graphs , 1998, IEEE Trans. Inf. Theory.

[14]  Julien Moncel.  Monotonicity of the minimum cardinality of an identifying code in the hypercube , 2006, Discret. Appl. Math..

[15]  Simon Litsyn,et al.  Exact Minimum Density of Codes Identifying Vertices in the Square Grid , 2005, SIAM J. Discret. Math..