For any integer $k>0$. a tree $T$ is $k$-cordial if there exists a labeling of the vertices of $T$ by $\mathbb{Z}_k$. inducing edge-weights as the sum modulo $k$ of the labels on incident vertices to a given edge. which furthermore satisfies the following conditions: \begin{enumerate}\item Each label appears on at most one more vertex than any other label. https://www.spidertattooz.com/