A note on $k$-cordial $p$-uniform hypertrees

TL;DR

This paper extends the concept of $k$-cordial labeling from trees to $p$-uniform hypertrees, providing new results for certain values of $k$ in hypergraph structures.

Contribution

It introduces the notion of $k$-cordial labelings for $p$-uniform hypertrees and establishes their existence for specific $k$ values, generalizing prior graph results.

Findings

$p$-uniform hypertrees are $k$-cordial for certain $k$ values

Generalizes $k$-cordial labeling from trees to hypergraphs

Provides partial results supporting the conjecture for hypergraphs

Abstract

Hovey introduced a $k$-cordial labeling of graphs as a generalization both of harmonious and cordial labelings. He proved that all tress are $k$-cordial for $k \in \{1,...,5\}$ and he conjectured that all trees are $k$-cordial for all $k$. \indent We consider a corresponding problem for hypergraphs, namely, we show that $p$-uniform hypertrees are $k$-cordial for certain values of $k$.