# Does this graph have a special name? (8-connected neighborhood)

Does this graph have a special name?

The vertices are arranged on a square square grid with a side length of $n$ and each inner vertices has an edge to its 8 neighbors.

And what about a similar graph with vertices arranged on a $n \times m$ rectangular grid?

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it looks like the union of Cartesian product and the categorical product of two paths – hbm Dec 20 '13 at 21:50

In terms of graph products the $n \times m$ grid will be the strong product of the path graphs $P_n$ and $P_m$, usually written as $P_n \boxtimes P_m$.