[PDF] a graph g is 2 edge connected if and only if

A graph is 2-edge-connected if it is connected and contains at least 2 vertices, but no bridge.
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  • How do you know if a graph is 2 edge connected?

    If the graph remains connected on removing every edge one by one then it is a 2-edge connected graph. To implement the above idea, remove an edge and perform Depth First Search(DFS) or Breadth-First Search(BFS) from any vertex and check if all vertices are covered or not.

  • What is a 2-connected graph in graph theory?

    2-Connected Graphs. Definition 1. A graph is connected if for any two vertices x, y ? V (G), there is a path whose endpoints are x and y. A connected graph G is called 2-connected, if for every vertex x ? V (G), G ? x is connected.

  • How to prove that a graph G is connected if and only if it has a spanning tree?

    Proof: Suppose that a simple graph G has a spanning tree T. T contains every vertex of G and there is a path in T between any two of its vertices. Because T is a subgraph of G, there is a path in G between any two of its vertices. Hence, G is connected.
  • The question that should immediately spring to mind is this: if a graph is connected and the degree of every vertex is even, is there an Euler circuit? The answer is yes. Theorem 5.2. 2 If G is a connected graph, then G contains an Euler circuit if and only if every vertex has even degree.
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