Abstract
Graph theory is one of the most important and basic topics of discrete mathematics in Mathematics. In all sectors of science graph theory has a great impact. The common use of graphs occurs in Computer Science, Physic, Biology, Finance and Chemistry except within Mathematics itself. Our main objective is to represent the cut-set, another type of subgraph of a connected graph. If deleting a certain number of edges from a graph makes it disconnected, then those set of deleted edges are called the cutset of the graph. Properties of cut-sets and its application will be discussed. When examining the characteristics of communication and transportation networks, cut-sets are crucial, for instance if we want to know if there are any network weak points that may be strengthened.
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