Let G be an infinite locally-finite connected graph roughly isometric to a tree, and o a fixed vertex of G. Given any p∈(0,1). Then under a mild condition, the number of surviving ends under Bernoulli-p bond percolation ω on G a.s. either is 0 or has the cardinality of the continuum; where a surviving end is an end of G induced by a surviving ray from o in the ω. This shows that Bernoulli-p bond percolations are roughly isometric invariant to a certain degree.

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