For example: enter image description here
Dividing between A and B: enter image description here
Would DAC and B be considered two subsets?
I am trying to create two subsets from an initial graph of 4 nodes.
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I would say that it is. A set can even be empty - obviously dividing beyond that point is unrewarding :) – 500 - Internal Server Error Dec 07 '22 at 21:57
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"A graph G is a finite nonempty set of objects called vertices together with a possibly empty set of unordered pairs of distinct vertices of G called edges."
"A graph H is a subgraph of a graph G if V(H) is a subset of V(G) and E(H) is a subset of E(G)"
-- both from Graph & Digraphs 2nd ed by Chartrand & Lesniak.
DAC and B are both subgraphs of the input graph. Neither is a subset since a graph isn't a set but a pair of sets as defined above. Note as per the definitions, a graph can have no edges, but must have at least one vertex.
Dave
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I'm guessing by subset you mean subgraph.
The answer is yes, a single isolated node is still a subgraph of the graph that contains that node.
Subgraphs can even be empty. The empty graph is a subgraph of all graphs.
Daniel
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