"Boreder" might be considered "legal" according to some guidelines, but is to be avoided because of the likely confusion with "border".
There is a hot "debate" on Twitter regarding whether the detention centers used by the US border patrol to detain/hold immigrants can be called "concentration camps" or not.
1 It depends on the morphology and the boundaries of the country. Coastal road/highway is an example of a road running along the border of a country partly surrounded by the sea. A more generic expression is border road!
The 'Home Counties' is the collective name given to the six counties which border London, but I am always at a loss as to whether to apply capitals.I think I will compose a question on this.
Generically, it could be called a frame, but a border around the sign could also be called a frame, so I don't think that's a good answer or what you're looking for.
On the other hand, a state border is a defined, measurable boundary, or perimeter. The conceptual "periphery" of a city center may lie within or outside of the city's state border, or perimeter. The NY Metro area, for example, includes peripheral suburbs in NJ and CT.
Edit, for clarity: In math, two distinct planes may intersect on a line, and 3 distinct planes may intersect at a point. Lines segments between two points are sometimes called edges. I said "square room", but what technically meant was "cube room". I said "corner where one of the walls meet the ceiling" because I was thinking of the phrase, "Stand with his nose in the corner." I've heard the ...