For every $n \geq 3$ consider a bipartite 3-regular graph $G_n$ with two parts $X=\{x_1, ..., x_n\}$ and $Y=\{y_1, ..., y_n\}$. For any $i \leq n$ assign either 0 or 1 to each vertex $x_i$, and denote it $\ell(x_i)$. For every $ i \leq n$ define $\ell(y_i)$ as follow: $\ell(y_i)=1$ if and only if the function $\ell(.)$ over at least 2 of neighbors of $y_i$ is 1. In other words, $\ell(y_i)$ takes the majority value of $\ell(.)$ over its neighbors. Finally, define the function $f_n: \{0, 1\}^n \rightarrow \{0, 1\}^n$ by $f\left(\ell(x_i), ..., \ell(x_n)\right):= \left(\ell(y_1), ..., \ell(y_n)\right)$. 

Can the family of function $\{f_n| n \in \mathbb{N}\}$ be a candidate for one-way functions, where $\{G_n| n \in \mathbf{N}\}$ is public? Has this family been studied before? Do you know of any references related to this?