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arXiv · 1411.5275

Identifying codes in vertex-transitive graphs and strongly regular graphs

Sylvain Gravier·Aline Parreau·Sara Rottey·Leo Storme·Elise Vandomme
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Abstract

We consider the problem of computing identifying codes of graphs and its fractional relaxation. The ratio between the size of optimal integer and fractional solutions is between 1 and 2 ln(|V|)+1 where V is the set of vertices of the graph. We focus on vertex-transitive graphs for which we can compute the exact fractional solution. There are known examples of vertex-transitive graphs that reach both bounds. We exhibit infinite families of vertex-transitive graphs with integer and fractional identifying codes of order |V|^a with a in {1/4,1/3,2/5}. These families are generalized quadrangles (strongly regular graphs based on finite geometries). They also provide examples for metric dimension of graphs.

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Sylvain Gravier, Aline Parreau, Sara Rottey, Leo Storme, Elise Vandomme. 2016-07-06. Identifying codes in vertex-transitive graphs and strongly regular graphs. https://arxiv.org/abs/1411.5275

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