Regular vertex $1$-extension for $2$-dimension meshes

In the paper, a schema of vertex $1$-extension for $2$-dimensional mesh is proposed. The extension is $4$-regular graph. The schema can be applied to meshes $n \times m$, $n \geq 2$ and $m \geq 2$. The extension is minimal for some meshes. Some extensions made by schema are not minimal. An example of such mesh is given.