Let G be a connected graph and let e be a cut edge in G. Let...

Let G be a connected graph and let e be a cut edge in G. Let K be the subgraph of G defined by:

V(K) = V(G) and

E(K) = E(G) - {e}

Prove that K has exactly two connected components. First prove that e cannot be a loop. Thus the endpoint set of e is of the form {v,w}, where v ≠ w. If ṽ∈V(K), prove that either there is a path in K from v to ṽ, or there is a path in K from w to ṽ

Expert Solution

Here in the given the graph if we delete the edge which is loop(as like e₇) then your graph G can't divide into 2 components

but this edge is not loop then graph G divide into 2 components in which there exits a path.

Colby Messinger answered 1 month ago

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