New results on the 1-isolation number of graphs without short cycles

Yirui Huang, Gang Zhang, Xian'an Jin

Let $G$ be a graph. A subset $D\subseteq V(G)$ is called a 1-isolating set of $G$ if $\Delta (G-N[D])\le 1$, that is, $G-N[D]$ consists of isolated edges and isolated vertices only. T…