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

A \emph{perfect Roman dominating function} (PRDF) on a graph $G = (V, E)$ isa function $f : V \rightarrow \{0, 1, 2\}$ satisfying the condition that everyvertex $u$ for which $f(u) = 0$ is adjacent to exactly one vertex $v$ for which$f(v) = 2$. The weight of a PRDF is the value $w(f) = \sum_{u \in V}f(u)$. Theminimum weight of a PRDF on a graph $G$ is called the \emph{perfect Romandomination number $\gamma_R^p(G)$} of $G$. A graph $G$ is perfect Romandomination domination stable if the perfect Roman domination number of $G$remains unchanged under the removal of any vertex. In this paper, wecharacterize all trees that are perfect Roman domination stable.

The characterization of perfect Roman domination stable trees