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 $G$ be a nontrivial connected graph of order $n$ and $k$ an integer with$2\leq k\leq n$. For a set $S$ of $k$ vertices of $G$, let $\kappa (S)$ denotethe maximum number $\ell$ of edge-disjoint trees $T_1,T_2,...,T_\ell$ in $G$such that $V(T_i)\cap V(T_j)=S$ for every pair $i,j$ of distinct integers with$1\leq i,j\leq \ell$. Chartrand et al. generalized the concept of connectivityas follows: The $k$-$connectivity$, denoted by $\kappa_k(G)$, of $G$ is definedby $\kappa_k(G)=$min$\{\kappa(S)\}$, where the minimum is taken over all$k$-subsets $S$ of $V(G)$. Thus $\kappa_2(G)=\kappa(G)$, where $\kappa(G)$ isthe connectivity of $G$.  This paper mainly focuses on the minimal number of edges of a graph $G$ with$\kappa_{3}(G)= 2$. For a graph $G$ of order $v(G)$ and size $e(G)$ with$\kappa_{3}(G)= 2$, we obtain that $e(G)\geq 6/5v(G)$, and the lower bound issharp by showing a class of examples attaining the lower bound.

The minimal size of a graph with generalized connectivity $\kappa_3 = 2$