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 connected graph, let $v\in V$ be a vertex and let $e=uw\inE$ be an edge. The distance between the vertex $v$ and the edge $e$ is given by$d_G(e,v)=\min\{d_G(u,v),d_G(w,v)\}$. A vertex $w\in V$ distinguishes two edges$e_1,e_2\in E$ if $d_G(w,e_1)\ne d_G(w,e_2)$. A set $S$ of vertices in aconnected graph $G$ is an edge metric generator for $G$ if every two edges of$G$ are distinguished by some vertex of $S$. The smallest cardinality of anedge metric generator for $G$ is called the edge metric dimension and isdenoted by $edim(G)$. In this article we introduce the concept of edge metricdimension and initiate the study of its mathematical properties. We make acomparison between the edge metric dimension and the standard metric dimensionof graphs while presenting some realization results concerning the edge metricdimension and the standard metric dimension of graphs. We prove that computingthe edge metric dimension of connected graphs is NP-hard and give someapproximation results. Moreover, we present some bounds and closed formulae forthe edge metric dimension of several classes of graphs.

Uniquely identifying the edges of a graph: the edge metric dimension