Word Count : 192

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False. Counterexample: take the star $G=K_{1,3}$ (one centre $v$ and three leaves). * The edge-connectivity $\kappa'(G)$ (minimum number of edges whose removal disconnects $G$) is $1$ — remove any one pendant edge and the corresponding leaf becomes isolated. ________ _____ _________ ____ ____ ________ _____.
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