What is a cut edge in graph theory?

In graph theory, a bridge, isthmus, cut-edge, or cut arc is an edge of a graph whose deletion increases the graph’s number of connected components. Equivalently, an edge is a bridge if and only if it is not contained in any cycle. For a connected graph, a bridge can uniquely determine a cut.

What is a cut Vertice?

(definition) Definition: A vertex whose deletion along with incident edges results in a graph with more components than the original graph. Also known as articulation point.

What is cut edge vertex cut?

A cut vertex is a vertex that when removed (with its boundary edges) from a graph creates more components than previously in the graph. A cut edge is an edge that when removed (the vertices stay in place) from a graph creates more components than previously in the graph.

What is cut set in a graph?

A cut set of a connected graph G is a set S of edges with the following properties. The removal of all edges in S disconnects G. The removal of some (but not all) of edges in S does not disconnects G.

How do you find the edge of a cut on a graph?

A cut edge e = uv is an edge whose removal disconnects u from v . Clearly such edges can be found in O(m^2) time by trying to remove all edges in the graph. We can get to O(m) based on the following two observations: All cut edges must belong to the DFS tree.

What are cut points in a graph?

A cutpoint (also known as an articulation point or cut-vertex) of an undirected graph, G is a vertex whose removal increases the number of components of G. Several generalizations to the directed case exist.

What is a cut set matrix?

A cut-set is a minimum set of branches of a connected graph such that when removed these branches from the graph, then the graph gets separated into 2 distinct parts called sub-graphs and the cut set matrix is the matrix which is obtained by row-wise taking one cut-set at a time.

What is a cut in a graph?

In graph theory, a cut is a partition of the vertices of a graph into two disjoint subsets. Any cut determines a cut-set, the set of edges that have one endpoint in each subset of the partition. These edges are said to cross the cut.