$\mathbb{Z}_{2}^{2}$-cordiality of complete and complete bipartite graphs

TL;DR

This paper characterizes when complete and complete bipartite graphs are $\

Contribution

It establishes precise conditions for $\

Findings

$K_{n}$ is $\

$K_{m,n}$ is $\

The results clarify the $\

Abstract

We prove that $K_{n}$ is $\mathbb{Z}_{2}^{2}$-cordial if and only if $1 \leq n \leq 3$ and that $K_{m,n}$ is $\mathbb{Z}_{2}^{2}$ if and only if it is false that $m=n=2$.