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

For two given non-negative integers $h$ and $k$, an $L(h,k)$-edge labeling ofa graph $G=(V(G),E(G))$ is a function $f':E(G) \xrightarrow{}\{0,1,\cdots, n\}$such that $\forall e_1,e_2 \in E(G)$, $\vert f'(e_1)-f'(e_2) \vert \geq h$ when$d'(e_1,e_2)=1$ and $\vert f'(e_1)-f'(e_2) \vert \geq k$ when $d'(e_1,e_2)=2$where $d'(e_1,e_2)$ denotes the distance between $e_1$ and $e_2$ in $G$. Here$d'(e_1,e_2)=k'$ if there are at least $(k'-1)$ number of edges in $E(G)$ toconnect $e_1$ and $e_2$ in $G$. The objective is to find \textit{span} which isthe minimum $n$ over all such $L(h,k)$-edge labeling and is denoted as$\lambda'_{h,k}(G)$. Motivated by the channel assignment problem in wirelesscellular network, $L(h,k)$-edge labeling problem has been studied in variousinfinite regular grids. For infinite regular octagonal grid $T_8$, it wasproved that $25 \leq \lambda'_{1,2}(T_8) \leq 28$ [Tiziana Calamoneri,International Journal of Foundations of Computer Science, Vol. 26, No. 04,2015] with a gap between lower and upper bounds. In this paper we fill the gapand prove that $\lambda'_{1,2}(T_8)= 28$.

Optimal $L(1,2)$-edge Labeling of Infinite Octagonal Grid