Bounds on the Maximum Number of Minimum Dominating Sets
Combinatorics
2013-08-15 v1
Abstract
We use probabilistic methods to find lower bounds on the maximum number, in a graph with domination number \gamma, of dominating sets of size \gamma. We find that we can randomly generate a graph that, w.h.p., is dominated by almost all sets of size \gamma. At the same time, we use a modified adjacency matrix to obtain lower bounds on the number of sets of a given size that do not dominate a graph on n vertices
Cite
@article{arxiv.1308.3210,
title = {Bounds on the Maximum Number of Minimum Dominating Sets},
author = {Samuel Connolly and Zachary Gabor and Anant Godbole and Bill Kay},
journal= {arXiv preprint arXiv:1308.3210},
year = {2013}
}
Comments
8 pages