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yakin
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How to find if a graph has a cut-edge/bridge and cut vertices. In other words, i am mixed up between cut edge and cut vertices? What is the difference and how one can find these in a graph?
yakin said:How to find if a graph has a cut-edge/bridge and cut vertices. In other words, i am mixed up between cut edge and cut vertices? What is the difference and how one can find these in a graph?
A cut edge is an edge in a graph that, when removed, disconnects the graph into two or more separate components. A cut vertex, on the other hand, is a vertex in a graph that, when removed, disconnects the graph into two or more separate components.
Cut edges and cut vertices both play a crucial role in determining the connectivity of a graph. Removing a cut edge or cut vertex can result in the graph being disconnected, while adding a cut edge or cut vertex can increase the connectivity of the graph.
Yes, it is possible for an edge to be both a cut edge and a cut vertex. This occurs when the edge connects two components of the graph and its removal results in the graph being disconnected into more than two components.
To identify a cut edge, you can use the concept of a bridge - an edge whose removal disconnects the graph. Cut vertices can be identified by using the concept of an articulation point - a vertex whose removal disconnects the graph.
Yes, cut edges and cut vertices are fundamental concepts in graph theory. They help us understand the connectivity of a graph and can be used to solve various graph-related problems, such as finding the shortest path between two vertices or determining the robustness of a network.