A connected graph can be separated into two parts by removing certain branches of the graph. This is equivalent to cutting a graph into two parts hence it is referred as cutset. A cutset is a minimal set of branches of a connected graph such that after removal of these branches graph gets separated into two distinct parts, each of which a connected graph with the condition that replacing any one branch from the cutset makes the graph connected.
The cutset separates the node of the graph into 2 group each being in one of its terminal’s incident at a node in one group and its other end at a node in the other group. So, we can consider that all the branches joined at a node forms a cutset since by removing them, the graph would be splitted into two parts.
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