Optimal accessing and non-accessing structures for graph protocols
Sylvain Gravier, Jérôme Javelle, Mehdi Mhalla, Simon Perdrix · arXiv (Cornell University) · 2011
An accessing set in a graph is a subset B of vertices such that there exists D subset of B, such that each vertex of V\B has an even number of neighbors in D. In this paper, we introduce new bounds on the minimal size kappa'(G) of an accessing set, and on the maximal size kappa(G) of a non-accessing set of a graph G. We show strong connections with perfect codes and give explicitly kappa(G) and kappa'(G) for several families of graphs. Finally, we show that the corresponding decision problems are NP-Complete.