K-edge-connected graph - meaning and definition. What is K-edge-connected graph
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What (who) is K-edge-connected graph - definition


K-edge-connected graph         
  • A 2-edge-connected graph
GRAPH THAT REMAINS CONNECTED WHENEVER FEWER THAN K EDGES ARE REMOVED
Edge connectivity; Edge-connectivity
In graph theory, a connected graph is -edge-connected if it remains connected whenever fewer than edges are removed.
Biconnected graph         
  • A biconnected graph on four vertices and four edges
  • A graph that is not biconnected. The removal of vertex x would disconnect the graph.
  • A biconnected graph on five vertices and six edges
  • A graph that is not biconnected. The removal of vertex x would disconnect the graph.
TYPE OF GRAPH
Bi-connected graph
In graph theory, a biconnected graph is a connected and "nonseparable" graph, meaning that if any one vertex were to be removed, the graph will remain connected. Therefore a biconnected graph has no articulation vertices.
K-vertex-connected graph         
  • A graph with connectivity 4.
GRAPH THAT CANNOT BE DISCONNECTED BY THE DELETION OF FEWER THAN K VERTICES
K-connected graph; Vertex connectivity
In graph theory, a connected graph is said to be -vertex-connected (or -connected) if it has more than vertices and remains connected whenever fewer than vertices are removed.