Geodesic
Regular vertex $1$-extension for $2$-dimension meshes
Prikladnaya Diskretnaya Matematika. Supplement, no. 14 (2021), pp. 161-163

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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.
Keywords: graph, mesh, fault tolerance, vertex extension. 
@article{PDMA_2021_14_a36,
     author = {A. A. Lobov and M. B. Abrosimov},
     title = {Regular vertex $1$-extension for $2$-dimension meshes},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {161--163},
     publisher = {mathdoc},
     number = {14},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2021_14_a36/}
}
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A. A. Lobov; M. B. Abrosimov. Regular vertex $1$-extension for $2$-dimension meshes. Prikladnaya Diskretnaya Matematika. Supplement, no. 14 (2021), pp. 161-163. http://geodesic.mathdoc.fr/item/PDMA_2021_14_a36/