Identifying codes in vertex-transitive graphs and strongly regular graphsReport as inadecuate

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(2015)ELECTRONIC JOURNAL OF COMBINATORICS.22(4). Mark 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 2ln(vertical bar V vertical bar) + 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 vertical bar V vertical bar(alpha) with alpha is an element of{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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Author: Sylvain Gravier, Aline Parreau, Sara Rottey , Leo Storme and √Člise Vandomme



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