Hamilton Paths in Dominating Graphs of Trees and Cycles
Combinatorics
2022-02-08 v2
Abstract
The dominating graph of a graph has as its vertices all dominating sets of , with an edge between two dominating sets if one can be obtained from the other by the addition or deletion of a single vertex of . In this paper we prove that the dominating graph of any tree has a Hamilton path. We also show how a result about binary strings leads to a proof that the dominating graph of a cycle on vertices has a Hamilton path if and only if .
Cite
@article{arxiv.2112.04448,
title = {Hamilton Paths in Dominating Graphs of Trees and Cycles},
author = {Kira Adaricheva and Heather Smith Blake and Chassidy Bozeman and Nancy E. Clarke and Ruth Haas and Margaret-Ellen Messinger and Karen Seyffarth},
journal= {arXiv preprint arXiv:2112.04448},
year = {2022}
}