How would you show that the edge connectivity for a uni-cyclic graph is no greater than 2?
I've tried to draw a few graphs first to see how I should approach it but not sure how.
Thanks
2026-03-26 08:04:37.1774512277
edge connectivity of a unicyclic graph?
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Here is a uni-cyclic graph:
You can delete any single edge and the remaining graph remains connected but if you delete two non-adjacent edges, the graph is no longer connected.
Here is another uni-cyclic graph:
You can find single edges (along the arms, for instance) that, when deleted, make the remaining graph non-connected. But you problem statement implies all uni-cyclic graphs, so it must hold for the above graph.