Among connected graphs, some are connected so slightly that removal of a single vertex or edge will disconnect them. Such vertices and edges are quite important. A vertex x is called a cutpoint in G if G — x contains more components than G does; in particular if G is connected, then a cutpoint is a vertex x such that G — x is disconnected. Similarly a bridge (or cut-edge) is an edge whose deletion increases the number of components.
KeywordsEdge Incident Single Vertex Block Graph Pendant Edge Critical Block
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