English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let $G=(V,E)$ be a graph. A subset $S \subseteq V$ is a dominating set of $G$if every vertex not in $S$ is adjacent to a vertex in $S$. A set $\tilde{D}\subseteq V$ of a graph $G=(V,E) $ is called an outer-connected dominating setfor $G$ if (1) $\tilde{D}$ is a dominating set for $G$, and (2) $G [V \setminus\tilde{D}]$, the induced subgraph of $G$ by $V \setminus \tilde{D}$, isconnected. The minimum size among all outer-connected dominating sets of $G$ iscalled the outer-connected domination number of $G$ and is denoted by$\tilde{\gamma}_c(G)$. We define the outer-connected bondage number of a graph$G$ as the minimum number of edges whose removal from $G$ results in a graphwith an outer-connected domination number larger than the one for $G$. Also,the outer-connected reinforcement number of a graph $G$ is defined as theminimum number of edges whose addition to $G$ results in a graph with anouter-connected domination number, which is smaller than the one for $G$. Thispaper shows that the decision problems for the outer-connected bondage and theouter-connected reinforcement numbers are $\mathbf{NP}$-hard. Also, the exactvalues of the bondage number are determined for several classes of graphs.

On the complexity of the outer-connected bondage and the outer-connected reinforcement problems