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Let S be a cut of a simple connected graph G.If S has no proper subset that is a cut, we say S is a minimal cut of G. To a minimal cut S, a connected component of G-S is called a fragment. And a fragment with no proper subset that is also a fragment is called an end. We characterized ends in our discussions and proved that to a connected graph G=(V,E), the number of its ends=|V(G)|.

Some results concerning the ends of minimal cuts of simple graphs