Discrete math Let G be a connected graph and let {a,b} be an edge in G. Prove th

Question

Discrete math
Let G be a connected graph and let {a,b} be an edge in G. Prove that the edge {a,b} is of a cycle if and only if its removal does not result in a disconnected graph. Discrete math
Let G be a connected graph and let {a,b} be an edge in G. Prove that the edge {a,b} is of a cycle if and only if its removal does not result in a disconnected graph.
Let G be a connected graph and let {a,b} be an edge in G. Prove that the edge {a,b} is of a cycle if and only if its removal does not result in a disconnected graph.

Explanation / Answer

G is connected graph and {a,b} be an edge in G..
suppose the edge {a,b} is of a cycle. Therefore if we remove that path, there must be another path connecting vertex a and vertex b, and so the graph will remain connected.
Conversely, suppose removal of an edge {a,b} does not result in disconnected graph. That is, there must be another path connecting those two vertics a and b, i.e, the edge {a,b} is nothing but a part of a cycle...

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