3-Factor-criticality in double domination edge critical graphs
Haichao Wang, Erfang Shan, Yancai Zhao · arXiv (Cornell University) · 2014
A vertex subset $S$ of a graph $G$ is a double dominating set of $G$ if $|N[v]\cap S|\geq 2$ for each vertex $v$ of $G$, where $N[v]$ is the set of the vertex $v$ and vertices adjacent to $v$. The double domination number of $G$, denoted by $γ_{\times 2}(G)$, is the cardinality of a smallest double dominating set of $G$. A graph $G$ is said to be double domination edge critical if $γ_{\times 2}(G+e)