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

Hovey introduced $A$-cordial labelings as a generalization of cordial andharmonious labelings \cite{Hovey}. If $A$ is an Abelian group, then a labeling$f \colon V (G) \rightarrow A$ of the vertices of some graph $G$ induces anedge labeling on $G$, the edge $uv$ receives the label $f (u) + f (v)$. A graph$G$ is $A$-cordial if there is a vertex-labeling such that (1) the vertex labelclasses differ in size by at most one and (2) the induced edge label classesdiffer in size by at most one. The problem of $A$-cordial labelings of graphscan be naturally extended for hypergraphs. It was shown that not every$2$-uniform hypertree (i.e., tree) admits a $Z_2\times Z_2$-cordial labeling\cite{Pechnik}. The situation changes if we consider $p$-uniform hypetrees fora bigger $p$. We prove that a $p$-uniform hypertree is $Z_2\times Z_2$-cordialfor any $p>2$, and so is every path hypergraph in which all edges have size atleast~3. The property is not valid universally in the class of hypergraphs ofmaximum degree~1, for which we provide a necessary and sufficient condition.

$Z_2\times Z_2$-cordial cycle-free hypergraphs