Identifying codes in vertex-transitive graphs and strongly regular graphs
Combinatorics
2016-07-07 v2 Discrete Mathematics
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.
Keywords
Cite
@article{arxiv.1411.5275,
title = {Identifying codes in vertex-transitive graphs and strongly regular graphs},
author = {Sylvain Gravier and Aline Parreau and Sara Rottey and Leo Storme and Elise Vandomme},
journal= {arXiv preprint arXiv:1411.5275},
year = {2016}
}