I am looking for an algorithm that finds minimal subset of vertices such that by removing this subset (and edges connecting these vertices) from graph all other vertices become unconnected (i.e. the graph won't have any edges).
I have a basic knowledge of graph theory so please excuse any incorrectness.
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cybermonkey There is no such a request for recommendation. This question is on-topic, and there is a clear answer to it (See AmiTavory's). (Obviously there are more answers, but none will be spam of opinionated answers). He is describing a problem, and he is getting an answer.
amit It asks for an algorithm, which is the same as 'code for me'.
cybermonkey No, it's not. Asking for algorithm is perfectly fine. Example 1, Example 2, Example 3, Example 4. It's perfectly fine to ask "How to do X", and asking for an algorithm is also on topic since it can be easily translated to any programming language. you can argue that the question does not show enough research effort - but that's another question.
The "most intuitive and greedy possible algorithm is" only "as good as it gets" when 1.2738^(subset_size) time is too long.