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arXiv · 1607.03848

Periodicity of identifying codes in strips

Minghui Jiang
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Abstract

An identifying code in a graph is a subset of vertices having a nonempty and distinct intersection with the closed neighborhood of every vertex. We prove that the infimum density of any identifying code in $S_k$ (an infinite strip of $k$ rows in the square grid) can always be achieved by a periodic identifying code with pattern length at most $2^{4k}$. Assisted by a compute program implementing Karp's algorithm for minimum cycle mean, we find a periodic identifying code in $S_4$ with the minimum density $11/28$, and a periodic identifying code in $S_5$ with the minimum density $19/50$.

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Minghui Jiang. 2016-07-13. Periodicity of identifying codes in strips. https://arxiv.org/abs/1607.03848

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