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I am trying to describe a region of a random walk on a graph (don't worry if you don't know what it is, visualise it as a physical space, e.g. a park). This graph has a part that if you go there, you cannot leave. I named this part "trapping".

I am trying to find a word for the other part, the one you can freely roam around but once you leave, you cannot come back. I thought of repelling, but repelling implies an action, that the part tries to get rid of you. I cannot find anything that fits here. Do you have any suggestions?

I'm also happy to change trapping to something else of it makes it easier to find an antonym.

Edit: This is for a paper I'm writing that has to do with random walks on a graph. I didn't want to scare people off with mathematical lingo, so I talked about physical space.

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    It's not the opposite is "trapping", but if the other area is where you would start you might call it "staging", which I think is a reasonable word for an area where you undertake various activities while preparing to depart.
    – nnnnnn
    Commented Aug 2, 2019 at 3:47
  • Is this graph part of a computer game? If so are there parts of the game outside the graph or, if you leave the area under discussion, have you left the game altogether until you start another session?
    – BoldBen
    Commented Aug 2, 2019 at 4:37
  • @BoldBen, no, it's part of a mathematical paper that has to do with a random walk on a graph.
    – tst
    Commented Aug 2, 2019 at 4:42
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    In that case 'lock-out area' might be appropriate, particularly if you renamed the 'trapping' area the 'lock in' area. I'm thinking that there is an analogy to leaving a building with an automatic lock without having a key to the lock or shutting your keys in a vehicle with an automatic lock. There is also the analogy of labour disputes where employers have been known to 'lock out' employees who are taking industrial action short of striking (a lock out) or where employees have occupied a workplace and refused to leave (a lock in).
    – BoldBen
    Commented Aug 2, 2019 at 10:59
  • @BoldBen that's great! Please write it as an answer.
    – tst
    Commented Aug 2, 2019 at 12:03

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As I have no references to include I originally posted this as a comment but the OP has asked me to post it as an answer.

The phrase 'lock-out area' might be appropriate, particularly if you renamed the 'trapping' area the 'lock in' area.

This works because there is an analogy to leaving a building with an automatic lock without having a key to the lock or shutting your keys in a vehicle with an automatic lock.

There is also the analogy of labour disputes where employers have been known to 'lock out' employees who are taking industrial action short of striking (a lock out) or where employees have occupied a workplace and refused to leave (a lock in).

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My immediate thought upon reading the title of the question was that the opposite of trapping should be releasing.

But what you're describing is something that's actually very similar to prohibiting.

From prohibit:

[Merriam-Webster]
1 : to forbid by authority : ENJOIN
2 a : to prevent from doing something
2 b : PRECLUDE

A sign that reads no entry allowed on a gate or door indicates that entry is prohibited.

Of course in this case, entry is allowed—but only once. As soon as you leave, you can never return again. I suppose it's a form of conditional prohibition.

A sign on the inside of the area, that you read as you leave, could be point of no return.

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One obvious candidate is anti-trapping, which has the advantage of being used in scientific literature (see e.g. here, here, here…).

Beyond that, here are some other possibilities: excluding, exiling, evicting, banishing, expatriating. It also makes me think of black and white holes.

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