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

Foucaud {\it et al.} recently introduced and initiated the study of a newgraph-theoretic concept in the area of network monitoring. Let $G$ be a graphwith vertex set $V(G)$, $M$ a subset of $V(G)$, and $e$ be an edge in $E(G)$,and let $P(M, e)$ be the set of pairs $(x,y)$ such that $d_G(x, y)\neqd_{G-e}(x, y)$ where $x\in M$ and $y\in V(G)$. $M$ is called a\emph{distance-edge-monitoring set} if every edge $e$ of $G$ is monitored bysome vertex of $M$, that is, the set $P(M, e)$ is nonempty. The {\emdistance-edge-monitoring number} of $G$, denoted by $\operatorname{dem}(G)$, isdefined as the smallest size of distance-edge-monitoring sets of $G$. For twographs $G,H$ of order $m,n$, respectively, in this paper we prove that$\max\{m\operatorname{dem}(H),n\operatorname{dem}(G)\}\leq\operatorname{dem}(G\,\Box \,H) \leqm\operatorname{dem}(H)+n\operatorname{dem}(G)-\operatorname{dem}(G)\operatorname{dem}(H)$, where $\Box$ is the Cartesianproduct operation. Moreover, we characterize the graphs attaining the upper andlower bounds and show their applications on some known networks. We also obtainthe distance-edge-monitoring numbers of join, corona, cluster, and somespecific networks.

Monitoring the edges of product networks using distances