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

The square $G^2$ of a graph $G$ is defined on the vertex set of $G$ in such away that distinct vertices with distance at most two in $G$ are joined by anedge. We study the chromatic number of the square of the Cartesian product$C_m\Box C_n$ of two cycles and show that the value of this parameter is atmost 7 except when $m=n=3$, in which case the value is 9, and when $m=n=4$ or$m=3$ and $n=5$, in which case the value is 8. Moreover, we conjecture thatwhenever $G=C_m\Box C_n$, the chromatic number of $G^2$ equals $\lceilmn/\alpha(G^2) \rceil$, where $\alpha(G^2)$ denotes the size of a maximalindependent set in $G^2$.

Coloring the square of the Cartesian product of two cycles